MSSURVIV User's Manual

James E. Hines
USGS, Patuxent Wildlife Research Center
12100 Beech Forest Rd
Laurel, MD 20708

email: jhines@usgs.gov

Introduction

Program MSSURVIV (Multi-State-SURVIVal analysis) computes parameter estimates of survival/transition and capture probability under the multistate models described in "Capture-recapture Studies for Multiple Strata including non-Markovian Transition Probabilities" (Brownie et. al., 1993). Actually, MSSURVIV is a specially modified version of Dr. G. White's program SURVIV (White, 1983) which incorporates the multistate models. With this program and it's companion program, CNVMEMOV, users are able to get parameter estimates for these complex models from capture-history data without having to specify the cell probabilities.

MSSURVIV is intended to be used in a situation where one is interested in not only survival and capture probabilities, but also transition probabilities (the probability of moving from one stratum to another). The strata may be defined as any discrete categories to which captured animals can be assigned at any given time. For example, strata may be based on such factors as capture location or individual variables such as breeding status or weight class. This situation may be thought of as a more general Jolly-Seber model where a matrix of survival/transition probabilities replaces a single survival rate and a vector of capture probabilities replaces a single capture probability. Output from MSSURVIV includes survival/movement probability estimates, capture probability estimates, goodness-of-fit tests, and likelihood-ratio tests. Estimates may be computed under the "Markovian" models or the "Non-Markovian/memory" models. The Markovian models assume that survival/transition probabilities of an animal depend on the stratum in which the animal is located at the beginning of the interval. The parameters under these models would be a matrix of survival/transition probabilities and a vector of capture probabilities for each time-period. Optionally, MSSURVIV may be instructed to decompose the combined survival/transition probabilities into separate survival and transition probabilities. Non-Markovian models assume that survival/transition probabilities for the interval (i, i+1) depend not only on stratum at time i, but also on stratum at i-1. These models produce much larger matrices of parameter estimates than Markovian models.

By default, three models are generated for either of these two model-sets. The three models are analogous to Models "D", "B", and "A" produced by program JOLLY for standard Jolly-Seber analysis (Pollock et. al., 1990). Model "D" computes estimates under the assumption that survival/transition probabilities and capture probabilities are constant over time. Model "B" assumes survival/transition probabilities are constant over time, but capture probabilities are time-dependent. Model "A" assumes both survival/transition and capture probabilities are time-dependent. If necessary, users may examine these models to generate statements for their own models.

The experimental situation to which this program applies is one in which animals are initially marked with a unique tag, and released. This process is repeated for each of the sampling periods. Information used to assign the animal to the proper stratum (eg. sex, weight, age, capture location, ...) is recorded for each capture of each animal. Using these data, the capture-history of each animal is generated consisting of codes indicating the status of the animal at each capture period. For example, if an animal were captured in stratum A in time-period 1, not captured in periods 2 and 3, and captured in stratum B in time-period 4, the capture history would be: "A 0 0 B". If the variable of interest is a continuous variable, cutpoints must be defined to break it into discrete strata (eg., weight -> weight-class) before the capture-history records can be generated.

Input to MSSURVIV consists of statements which define the capture data and statements defining the selected model structure. The format of the input file is the same as for program SURVIV except that no cell probabilities need be given. The statements defining the data consist of the number of animals captured and released in each time-period and stratum, and the number next recaptured in each subsequent time-period and stratum. Statements which set parameters equal to other parameters define model structure.

Although MSSURVIV eliminates the need for specifying cell probabilities, the job of summarizing capture-history records and defining model structure can be very complicated and can lead to errors. Program CNVMEMOV was created to automate this process. CNVMEMOV reads as input the capture-history records and produces all of the statements necessary to run program MSSURVIV under the "Markovian" or "memory" model sets described above.

Using CNVMEMOV

To run CNVMEMOV, type CNVMEMOV at the DOS prompt and respond to the program prompts. When the program is run, the following should appear on the screen:

Program CNVMEMOV - Converts "Capture-history" data into
                   MSSURVIV input data
 
 Date compiled: 1/23/98
 
 Programmer: James E. Hines
             Biological Research Div., USGS
             11510 American Holly Dr. #201
             Patuxent Wildlife Research Center
             Laurel, MD. 20708-4017
             email: jim_hines%40usgs.gov
 
 Version 2.0 - added capability for >2 age-classes
               added capability for >1 group      
 
 ** Note: The order of age-classes in old version was
          ADULT followed by YOUNG.  In this version
          the order must be from youngest to oldest.
 ** Also: The old version used "GROUP" as a synonym of
          "STRATA".  (That was stupid!)  In this version
          "STRATA" are the transitional states and 
          "GROUPS" are the separate classification 
          of animals to/from which animals cannot move.
          Examples of STRATA might be location,
          breeding-status, weight-class.
          Examples of GROUP might be sex, species.

After this informatory text is printed, CNVMEMOV attempts to open an output file called CNVMEMOV.OUT. This is the file which will contain the summarized data to be input to program MSSURVIV. If this file already exists (from a previous run) the program will ask if it is OK to overwrite this file. If "y" or "Y" is typed, CNVMEMOV will proceed. Any other response will abort the program.

*** Output file (CNVMEMOV.OUT) exists!, overwrite(Y/N)? Y

The next prompt is for the name of the input file containing the capture-history records. Respond with any legal filename, including drive and subdirectory if not in the current directory.

Enter the name of the file containing the capture-history records FILE:C:\MSSRV\SAMPLE.DAT

If the input file does not exist, CNVMEMOV will print an error message and abort. If it does exist, the first five lines of the file will be displayed on the screen. This helps the user find the column numbers needed for later prompts.

              FILE:C:\MSSRV\SAMPLE.DAT                                                      
         1         2         3         4         5         6         7
....5....0....5....0....5....0....5....0....5....0....5....0....5....0
A000  491
A00A   15
A00B   12
A00C   11
A0A0   37
......................................................................

The next prompt is for the number of strata and time-periods. The program requires that you enter two numbers separated by a comma, e.g.,

Enter the number of strata, time-periods, age-classes and groups:
STRATA,TIME-PERIODS,AGE-CLASSES,GROUPS(eg 3,7,1,1):3,4,1,1

In this example, there are 4 capture periods, 3 strata (designated A, B, and C), 1 age-class and 1 group. The next prompt is for the codes representing each stratum. These are the codes which represent each of the strata of capture in the capture-history records. Any character other than the ones in this list indicate that the animal was not captured in a time-period. Selected strata may be omitted from an analysis by not including them in the this list. Any single character may be used to represent each of the strata, e.g.,

Enter the codes representing each strata:
 (If upper case in input file, type upper case here.)
STRATA CODES(no quotes or spaces- eg 123):ABC

CNVMEMOV will distinguish between lower and upper case characters for these codes, so it is imperative that these codes match the codes in the data file. If "abc" were entered instead of "ABC", none of the captures would be used.

The next prompt asks for the column numbers containing stratum codes for each time period. The first five lines of data have been listed previously to help locate the column numbers, e.g.,

If strata codes are in consecutive columns, enter the
 column number of the first strata code,
Or enter 0 if they are not sequential
FIRST COLUMN OF STRATA CODES:1

The next prompt asks for the column number containing the fate on last capture. If the data set contains a field indicating whether animals were released or not released (e.g., dead in trap), the column number of this field would be entered here. If there is no such field in the data, enter 0 and it will be assumed that all animals were released on last capture. Any non-blank character in this column indicates that the animals were not released on last capture.

Enter column number containing fate on last capture, or
      0 if all captured animals were always released.
Note: Any non-blank character in this column is
      interpreted as indicating that the animal was
      not released
FATE COLUMN:0

If more than one group was specified in the earlier prompt, the next prompt would ask for the column number containing the group of the animals. If the data set contains a field indicating a group the animals belong to, (e.g. sex, size), the column number of this field would be entered here. As with the strata codes, upper/lower case is significant here.

Enter the column number containing the GROUP code,
GROUP COLUMN:
Enter groupe-codes
  (eg. MF for male, female)
GROUP-CODES:

The next prompt is for the starting column of a frequency variable. If the capture-histories are summarized, the data will contain a frequency variable for each capture-history and the starting column is entered here. If the data are not summarized (i.e., one record per animal), enter 0 for the starting column, e.g.,

Enter starting column of cap-history frequency, or
      0 if capture-histories are not summarized.
STARTING COLUMN:6

If a number greater than zero is entered for the frequency starting column, CNVMEMOV will prompt for the ending column of the frequency variable.

The next prompt is for the selection of model sets to be run with MSSURVIV. One or both of the model sets may be chosen, e.g.,

Enter 1 for the "MEMORY-MOVEMENT model set
      2 for the "MOVEMENT-ONLY model set
      3 for both model sets
      4 for the "MOVEMENT-ONLY model set w/ S-M parameterization
MODEL SETS (1,2,3, or 4):4

In some cases, it is desirable to compute estimates in terms of separate survival rate and movement probabilities rather than with transition probabilities that include both survival and movement. If we assume survival from time i to i+1 does not depend on stratum in time-period i+1, then we can rewrite Φirs as Φirs = SirΨirs, where Ψirs is the conditional probability that an animal in stratum r at time i is in stratum s at time i+1, given that the animal is alive at i+1. The sum of the survival/transition probabilities is equal to the survival rate (i.e., ΣSΦirs = Sir, where Φirs is the probability that an animal alive in stratum r at period i is alive and in stratum s at period i+1, and Sir is the probability that an animal in stratum r at time i is alive at period i+1.) In a k-stratum experiment, we can compute a survival rate and k movement probabilities for each stratum and time-interval from the k transition probabilities, Φirs. This computation may be done from the output for the movement-only model set, however the computation of variances would be very difficult. MSSURVIV can be instructed to treat survival rate and movement probabilities as separate parameters instead of combined transition probabilities in order to produce the desired estimates and variances. I have called this the "S-M parameterization" for the estimation of separate survival and movement parameters.

If the "MOVEMENT-ONLY model set with S-M parameterization" is chosen, CNVMEMOV will prompt for a stratum number. This number controls which movement probability is replaced by the survival probability in the output parameters. For the S-M parameterization, the k×k survival/movement estimates for each time-period will be changed to N survival estimates and k×(k-1) movement estimates. Since the sum of the movement probabilities for any cohort must equal 1.0, one of the movement parameters is not needed (i.e., it is obtained as 1 minus the sum of the others). Any of the k movement parameters may be omitted, however, the optimization routine in MSSURVIV works better if the parameters are not close to 0.0 or 1.0. For this reason, the best movement parameter to omit is the one closest to 0.0 or 1.0.

For the S-M parameterization, one of the 3
movement parameters must be replaced by the survival
parameter.  Choose 0 to replace the diagonal parameter
(probability of returning to a stratum), or the index
of one of the 3 strata.
Stratum (0 or 1-3)?3

By choosing 3, CNVMEMOV will produce the statements to cause MSSURVIV to use the "S-M parameterization" of the movement-only model set. Instead of a 3×3 matrix of survival/movement probability estimates, MSSURVIV will compute 3 survival rate estimates and 6 movement probabilities for each time period. The 9 parameters for time i are:

The probability of moving from any stratum, X, to stratum C must be computed by subtracting the sum of ΨiXA and ΨiXB from 1.0.

The next prompt is for a title to appear on the output. Any string of characters (not including quotes) is acceptable as long as the length is less than 256, e.g.,

Enter a title to appear on the MSSURVIV output
TITLE(no quotes):MSSURVIV SAMPLE DATA (SAMPLE.DAT)

CNVMEMOV will output the number of records read and the total number of transitions. The total number of transitions can be used to determine if some of the strata need to be combined to help with convergence problems (See section on sparse data).

Here is the file created by CNVMEMOV which can be input to MSSURVIV:

PROC TITLE 'expected value data w/ 2 groups';
PROC MODEL NPAR=0036 ADDCELL NAGE=1 NYRS=04 STRATA=2 NGROUPS=2
  PHIMISS=2;
COHORT=1000;236:;102:;76:;79:;22:;42:;
COHORT=1001;0:;338:;0:;156:;0:;64:;
COHORT=1236;267:;114:;77:;80:;
COHORT=1440;0:;444:;0:;183:;
COHORT=1343;260:;111:;
COHORT=1793;0:;495:;
COHORT=1000;62:;41:;11:;18:;2:;7:;
COHORT=1001;0:;105:;0:;29:;0:;8:;
COHORT=1062;74:;50:;14:;23:;
COHORT=1146;0:;135:;0:;40:;
COHORT=1085;83:;56:;
COHORT=1232;0:;158:;
LABELS;
S(001)=MOV(01,A,M) AA ;
S(002)=SRV(01,A,M) A ;
S(003)=MOV(01,A,M) BA ;
S(004)=SRV(01,A,M) B ;
S(005)=MOV(02,A,M) AA ;
S(006)=SRV(02,A,M) A ;
S(007)=MOV(02,A,M) BA ;
S(008)=SRV(02,A,M) B ;
S(009)=MOV(03,A,M) AA ;
S(010)=SRV(03,A,M) A ;
S(011)=MOV(03,A,M) BA ;
S(012)=SRV(03,A,M) B ;
S(013)=p(02,A,M) A ;
S(014)=p(02,A,M) B ;
S(015)=p(03,A,M) A ;
S(016)=p(03,A,M) B ;
S(017)=p(04,A,M) A ;
S(018)=p(04,A,M) B ;
S(019)=MOV(01,A,F) AA ;
S(020)=SRV(01,A,F) A ;
S(021)=MOV(01,A,F) BA ;
S(022)=SRV(01,A,F) B ;
S(023)=MOV(02,A,F) AA ;
S(024)=SRV(02,A,F) A ;
S(025)=MOV(02,A,F) BA ;
S(026)=SRV(02,A,F) B ;
S(027)=MOV(03,A,F) AA ;
S(028)=SRV(03,A,F) A ;
S(029)=MOV(03,A,F) BA ;
S(030)=SRV(03,A,F) B ;
S(031)=p(02,A,F) A ;
S(032)=p(02,A,F) B ;
S(033)=p(03,A,F) A ;
S(034)=p(03,A,F) B ;
S(035)=p(04,A,F) A ;
S(036)=p(04,A,F) B ;
PROC ESTIMATE NOVAR NSIG=6 MAXFN=64000 NAME=MODL_D;
INITIAL; ALL= 0.500;
CONSTRAINTS;
S(005)=S(001) /* MOV(02,A,M) AA=MOV(01,A,M) AA */;
S(006)=S(002) /* SRV(02,A,M) A =SRV(01,A,M) A  */;
S(007)=S(003) /* MOV(02,A,M) BA=MOV(01,A,M) BA */;
S(008)=S(004) /* SRV(02,A,M) B =SRV(01,A,M) B  */;
S(009)=S(001) /* MOV(03,A,M) AA=MOV(01,A,M) AA */;
S(010)=S(002) /* SRV(03,A,M) A =SRV(01,A,M) A  */;
S(011)=S(003) /* MOV(03,A,M) BA=MOV(01,A,M) BA */;
S(012)=S(004) /* SRV(03,A,M) B =SRV(01,A,M) B  */;
S(015)=S(013) /* p(03,A,M) A   =p(02,A,M) A    */;
S(016)=S(014) /* p(03,A,M) B   =p(02,A,M) B    */;
S(017)=S(013) /* p(04,A,M) A   =p(02,A,M) A    */;
S(018)=S(014) /* p(04,A,M) B   =p(02,A,M) B    */;
S(023)=S(019) /* MOV(02,A,F) AA=MOV(01,A,F) AA */;
S(024)=S(020) /* SRV(02,A,F) A =SRV(01,A,F) A  */;
S(025)=S(021) /* MOV(02,A,F) BA=MOV(01,A,F) BA */;
S(026)=S(022) /* SRV(02,A,F) B =SRV(01,A,F) B  */;
S(027)=S(019) /* MOV(03,A,F) AA=MOV(01,A,F) AA */;
S(028)=S(020) /* SRV(03,A,F) A =SRV(01,A,F) A  */;
S(029)=S(021) /* MOV(03,A,F) BA=MOV(01,A,F) BA */;
S(030)=S(022) /* SRV(03,A,F) B =SRV(01,A,F) B  */;
S(033)=S(031) /* p(03,A,F) A   =p(02,A,F) A    */;
S(034)=S(032) /* p(03,A,F) B   =p(02,A,F) B    */;
S(035)=S(031) /* p(04,A,F) A   =p(02,A,F) A    */;
S(036)=S(032) /* p(04,A,F) B   =p(02,A,F) B    */;
PROC ESTIMATE NOVAR NSIG=6 MAXFN=64000 NAME=MODL_B;
INITIAL; RETAIN=MODL_D; CONSTRAINTS;
S(005)=S(001) /* MOV(02,A,M) AA=MOV(01,A,M) AA */;
S(006)=S(002) /* SRV(02,A,M) A =SRV(01,A,M) A  */;
S(007)=S(003) /* MOV(02,A,M) BA=MOV(01,A,M) BA */;
S(008)=S(004) /* SRV(02,A,M) B =SRV(01,A,M) B  */;
S(009)=S(001) /* MOV(03,A,M) AA=MOV(01,A,M) AA */;
S(010)=S(002) /* SRV(03,A,M) A =SRV(01,A,M) A  */;
S(011)=S(003) /* MOV(03,A,M) BA=MOV(01,A,M) BA */;
S(012)=S(004) /* SRV(03,A,M) B =SRV(01,A,M) B  */;
S(023)=S(019) /* MOV(02,A,F) AA=MOV(01,A,F) AA */;
S(024)=S(020) /* SRV(02,A,F) A =SRV(01,A,F) A  */;
S(025)=S(021) /* MOV(02,A,F) BA=MOV(01,A,F) BA */;
S(026)=S(022) /* SRV(02,A,F) B =SRV(01,A,F) B  */;
S(027)=S(019) /* MOV(03,A,F) AA=MOV(01,A,F) AA */;
S(028)=S(020) /* SRV(03,A,F) A =SRV(01,A,F) A  */;
S(029)=S(021) /* MOV(03,A,F) BA=MOV(01,A,F) BA */;
S(030)=S(022) /* SRV(03,A,F) B =SRV(01,A,F) B  */;
PROC ESTIMATE NOVAR NSIG=6 MAXFN=64000 NAME=MODL_A;
INITIAL; RETAIN=MODL_B; CONSTRAINTS;
S(017)=1.0 /* p(04,A,M) A    */;
S(018)=1.0 /* p(04,A,M) B    */;
S(035)=1.0 /* p(04,A,F) A    */;
S(036)=1.0 /* p(04,A,F) B    */;
PROC ESTIMATE NOVAR NSIG=6 MAXFN=64000 NAME=1GRP_A;
INITIAL; RETAIN=MODL_A; CONSTRAINTS;
S(019)=S(001) /* MOV(01,A,F) AA=MOV(01,A,M) AA */;
S(020)=S(002) /* SRV(01,A,F) A =SRV(01,A,M) A  */;
S(021)=S(003) /* MOV(01,A,F) BA=MOV(01,A,M) BA */;
S(022)=S(004) /* SRV(01,A,F) B =SRV(01,A,M) B  */;
S(023)=S(005) /* MOV(02,A,F) AA=MOV(02,A,M) AA */;
S(024)=S(006) /* SRV(02,A,F) A =SRV(02,A,M) A  */;
S(025)=S(007) /* MOV(02,A,F) BA=MOV(02,A,M) BA */;
S(026)=S(008) /* SRV(02,A,F) B =SRV(02,A,M) B  */;
S(027)=S(009) /* MOV(03,A,F) AA=MOV(03,A,M) AA */;
S(028)=S(010) /* SRV(03,A,F) A =SRV(03,A,M) A  */;
S(029)=S(011) /* MOV(03,A,F) BA=MOV(03,A,M) BA */;
S(030)=S(012) /* SRV(03,A,F) B =SRV(03,A,M) B  */;
S(031)=S(013) /* p(02,A,F) A   =p(02,A,M) A    */;
S(032)=S(014) /* p(02,A,F) B   =p(02,A,M) B    */;
S(033)=S(015) /* p(03,A,F) A   =p(03,A,M) A    */;
S(034)=S(016) /* p(03,A,F) B   =p(03,A,M) B    */;
S(017)=1.0 /* p(04,A,M) A    */;
S(035)=1.0 /* p(04,A,F) A    */;
S(018)=1.0 /* p(04,A,M) B    */;
S(036)=1.0 /* p(04,A,F) B    */;
PROC TEST; PROC STOP;

The output file, CNVMEMOV.OUT, contains a title statement, statements to define the input data, label definitions, statements to describe models, a test statement and a stop statement. The title statement is used to identify the data used in the analysis.

The model definition statements start with "PROC MODEL NPAR=0036 ADDCELL NAGE=1 NYRS=04 STRATA=2 NGROUPS=2 PHIMISS=2;" and end with "COHORT=1232;0:;158:; ". The "NPAR=36" indicates the maximum number of parameters (estimated or fixed) in any of the following models. In this example there are 4 (2×2) transition probability parameters for each of the 3 intervals (4 sample periods), giving 12 parameters per group. There are 2 capture probabilities for each period (not including the first) giving 6 parameters per group. So, the total number of paramters is 12x2+6x2=36. The NAGE, NYRS, STRATA, and NGROUPS keywords indicate the respective values for each, and PHIMISS indicates which of the transitions is to be computed by subtraction. In this case, PHIMISS=2 indicates that transitions to the 2nd strata are to be computed as 1 - the probability of moving to the first strata.

The rest of the model definition statements contains the summary data in a form which could be thought of as a generalized "Leslie Method-B Table" or "m-array" where each 2×2 matrix is treated as one element in the m-array. Each of the records starts with "COHORT=x" where x is the number of animals released in a stratum and year. The numbers that follow indicate the number of recaptures in succeeding periods and strata. Figure 1 shows the structure of the m-array for these data.

Figure 1.

R1   M1,2   M1,3   M1,4
R2          M2,3   M2,4
R3                M3,4

Ri = (Ri1 Ri2)

     (Mi1,1 Mi1,2)
Mi = (Mi2,1 Mi2,2)
where Rir=number released in time i, stratum r, and Mi,jrs=number captured in time j in stratum s, last captured in time i in stratum r.

From the output file, the numbers of animals released in time period 1 are: 1000 from stratum 1 and 1001 from stratum 2. The matrix of recaptures in time period 2 of animals captured in time period 1 is:

              [236 102]
        M1,2 = [0   338]
        
Of the 676 animals captured in time period 2 which were also captured in time period 1, 236 animal started in stratum 1 and stayed in stratum 1, 102 animals started in 1 and moved to 2. (Row indicates stratum of previous capture. Column indicates stratum of capture.) 0 animals moved from 2 to 1 and 338 moved from 2 to 2.

The next 2 columns of rows 1-2 in the data are the matrix of transitions of animals captured in time period 3 that were last captured in time period 1 (not captured in time period 2). The last 2 columns in the first 2 rows form the matrix of transitions of animals captured in time period 4 which were last captured in time period 1 (not captured in time periods 2 or 3).

Following the data are the labels for each of the parameters. Internally, the parameters are called "S(1), S(2), ... S(NPAR). The labels relate these internal parameters to meaningful labels for these models. If the "Movement-only" model was chosen, the transition probabilities are labeled "PHI" followed by the time period in parenthesis and the transition. So, "PHI(01) AB" is the probability of survival from time period one to time period two and moving from stratum "A" to stratum "B". If the "Memory-movement" models were chosen, there will be three strata following the time period for each "PHI" since transition in time period i depends on stratum of capture in time period i-1 as well as in time period i. If the S-M parameterization is chosen, the survival parameter (SRV) will be followed by time period, age, and group in parenthesis, followed the stratum of capture in time period i. The movement parameters (MOV) will be followed by the time period, age, and group in parenthesis, then stratum in time period i and stratum in period i+1.

In all models, capture-probability parameters are labeled "p" and are followed by time period of capture, age, and group in parentheses, and stratum of capture.

After the label definitions come the model definitions for each model. Each model starts with a "PROC ESTIMATE" statement. Options on the "PROC ESTIMATE" statement include "NOVAR" which inhibits printing of the variance-covariance matrix, the number of significant digits, "NSIG" (i.e., number of digits following the decimal point which do not change at the end of the iterative process), the maximum number of function evaluations, "MAXFN", and the name of the model. If the variance-covariance matrix of parameter estimates is desired, delete the string "NOVAR" using a text editor.

CNVMEMOV produces the model definitions from most restrictive (model "D") to most general (model "A"). The reason for this is that the most restrictive model has the fewest estimable parameters and converges more easily. Final estimates from this model can then be input as starting values to more general models. MSSURVIV requires starting values for all models and CNVMEMOV sets all parameters to 1/(# of strata) for the first model to ensure that the estimates of transition probability are less than or equal to 1.0. (INITIAL; ALL=0.333;).

The statements following the "CONSTRAINTS" statement describe each model in terms of the most general model. In model "D", the survival and movement probabilities are assumed to be constant across time, so the survival and movement probabilities for time period two and three are set equal to the survival and movement probabilities for time period one. The capture probabilities are also assumed constant over time, so the capture probabilities for time periods 3 and 4 are set equal to the capture probabilities for time period 2. These equalities must be specified in terms of parameter number which can be obtained from the labels section. In the example, the first constraint is "S(005)=S(001);". A comment appears immediately after the constraint which indicates which parameters are constrained.

The sequence of statements starting with "PROC ESTIMATE ... NAME=MODL_B" cause MSSURVIV to produce estimates under the model with time-specific capture probabilities and constant survival and movement probabilities. The initial values are set equal to the final values obtained for model "D" (INITIAL; RETAIN=MODL_D;), and the constraints on the survival and movement probability parameters are the same as for model "D". Since capture probabilities may vary with time, there are no constraints on the capture probability parameters.

Statements for model "A" follow model "B". Model "A" assumes time-specific survival and movement probabilities and time-specific capture probabilities. Since there is no information on animals after the last time period, the last survival and movement probabilities and last capture probabilities cannot be separately estimated under model "A". For this reason, the last capture probability parameters have to be constrained to a constant. This causes the last survival/movement probability estimates to be the product of survival and movement and capture-probability for this model.

If more than one group is to be analyzed, CNVMEMOV produces one other model which is equivalent to model A except that the parameters are constrained equal across groups.

The "PROC TEST;" statement causes MSSURVIV to print tables of statistics used for comparison of the models. "PROC STOP;" causes MSSURVIV to stop execution even if more statements follow. MSSURVIV

MSSURVIV prompts for one line of input to specify the name of the input and output files and command line options. When the program is run, the following prompt appears:

Enter command line parameters [i=in_file] [l=out_file]
   [lines=n] [compile run] [noecho]:
At this prompt, any or all of the items enclosed in brackets may be specified. If "i=in_file" is specified, the input will be read from the file "in_file". Usually, this is the file created by CNVMEMOV and is called CNVMEMOV.OUT unless it has been renamed. A full pathname may be used to indicate a different directory. If this item is omitted, MSSURVIV expects the input from the keyboard. (Cntl-Break will abort the program).

If "l=out_file" is specified, output from MSSURVIV will be directed to the file "out_file". The default output file is the CRT screen. To direct output directly to the printer, use "l=lpt1".

If "lines=n" is included, MSSURVIV will print a header and the title in the output file after every n lines. The default value for n is 9999.

The "noecho" option causes MSSURVIV to suppress printing of the input data. This option is useful when there are several runs of models on the same data and you would like to conserve paper, but at least one run should contain a listing of the data to check for "typos".

To run the sample data file with MSSURVIV, enter the following at the above prompt:

i=cnvmemov.out l=sample.out

The output produced by MSSURVIV contains a listing of the input data, estimates of the parameters under each model, a goodness-of-fit test for each model, an AIC statistic for each model, and between model tests. The following output was created using MSSURVIV on the sample data file listed previously:

MSSURVIV - Survival Rate Estimation with User Specified Cell Probabilities
 28-Jan-98      11:20:03         Ver 2.0             01/01/98        Page  001

  INPUT --- PROC TITLE 'SADF';

     CPU time in seconds for last procedure was    0.00

  INPUT --- PROC MODEL NPAR=0036 ADDCELL NAGE=1 NYRS=04 STRATA=2 
  INPUT --- NGROUPS=2 PHIMISS=2;

  INPUT ---    COHORT=1000; 236:;102:;76:;79:;22:;42:;
  INPUT ---    COHORT=1001; 0:;338:;0:;156:;0:;64:;
  INPUT ---    COHORT=1236; 267:;114:;77:;80:;
  INPUT ---    COHORT=1440; 0:;444:;0:;183:;
  INPUT ---    COHORT=1343; 260:;111:;
  INPUT ---    COHORT=1793; 0:;495:;
  INPUT ---    COHORT=1000; 62:;41:;11:;18:;2:;7:;
  INPUT ---    COHORT=1001; 0:;105:;0:;29:;0:;8:;
  INPUT ---    COHORT=1062; 74:;50:;14:;23:;
  INPUT ---    COHORT=1146; 0:;135:;0:;40:;
  INPUT ---    COHORT=1085; 83:;56:;
  INPUT ---    COHORT=1232; 0:;158:;
 
  INPUT --- PROC ESTIMATE NOVAR NSIG=6 MAXFN=64000 NAME=MODL_D;
      Number of parameters in model  =  36

      Number of parameters set equal =  24

      Number of parameters fixed     =   0

      Number of parameters estimated =  12

     Final function value  11038.617     (Error Return = 130)

     Number of significant digits        5

     Number of function evaluations    834

 * *  WARNING  * *   Rounding errors became dominant before parameters estimated

 * *  WARNING  * *   to NSIG digits for Model MODL_D    

 * *  WARNING  * *   Check to be sure the parameters are identifiable,

 * *  WARNING  * *   but the problem may just be ill-conditioned.

   Cohort  Cell   Observed  Expected  Chi-square  Note
   ------  ----   --------  --------  ----------  -------------
      1      1      236.     213.083      2.465   0 < P < 1      
      1      2      102.      91.077      1.310   0 < P < 1      
      1      3       76.      70.554      0.420   0 < P < 1      
      1      4       79.      73.626      0.392   0 < P < 1      
      1      5       22.      23.361      0.079   0 < P < 1      
      1      6       42.      45.126      0.217   0 < P < 1      
      1      7      443.     483.173      3.340   0 < P < 1      
      1 Cohort df=  6                     8.223   P = 0.2222
      2      2      338.     301.610      4.391   0 < P < 1      
      2      4      156.     143.954      1.008   0 < P < 1      
      2      6       64.      68.707      0.322   0 < P < 1      
      2      7      443.     486.730      3.929   0 < P < 1      
      2 Cohort df=  3                     9.650   P = 0.0218
      3      1      267.     263.370      0.050   0 < P < 1      
      3      2      114.     112.571      0.018   0 < P < 1      
      3      3       77.      87.205      1.194   0 < P < 1      
      3      4       80.      91.002      1.330   0 < P < 1      
      3      5      698.     681.852      0.382   0 < P < 1      
      3 Cohort df=  4                     2.975   P = 0.5620
      4      2      444.     433.884      0.236   0 < P < 1      
      4      4      183.     207.086      2.801   0 < P < 1      
      4      5      813.     799.030      0.244   0 < P < 1      
      4 Cohort df=  2                     3.282   P = 0.1938
      5      1      260.     286.170      2.393   0 < P < 1      
      5      2      111.     122.316      1.047   0 < P < 1      
      5      3      972.     934.514      1.504   0 < P < 1      
      5 Cohort df=  2                     4.944   P = 0.0844
      6      2      495.     540.246      3.789   0 < P < 1      
      6      3     1298.    1252.754      1.634   0 < P < 1      
      6 Cohort df=  1                     5.424   P = 0.0199
      7      1       62.      69.693      0.849   0 < P < 1      
      7      2       41.      46.448      0.639   0 < P < 1      
      7      3       11.      11.855      0.062   0 < P < 1      
      7      4       18.      20.221      0.244   0 < P < 1      
      7      5        2.       2.017      0.000   0 < P < 1      
      7      6        7.       6.708      0.013   0 < P < 1      
      7      7      859.     843.057      0.301   0 < P < 1      
      7 Cohort df=  6                     2.108   P = 0.9095
      8      2      105.     118.159      1.466   0 < P < 1      
      8      4       29.      31.341      0.175   0 < P < 1      
      8      6        8.       8.313      0.012   0 < P < 1      
      8      7      859.     843.186      0.297   0 < P < 1      
      8 Cohort df=  3                     1.949   P = 0.5831
      9      1       74.      74.014      0.000   0 < P < 1      
      9      2       50.      49.328      0.009   0 < P < 1      
      9      3       14.      12.590      0.158   0 < P < 1      
      9      4       23.      21.475      0.108   0 < P < 1      
      9      5      901.     904.592      0.014   0 < P < 1      
      9 Cohort df=  4                     0.290   P = 0.9905
     10      2      135.     135.275      0.001   0 < P < 1      
     10      4       40.      35.881      0.473   0 < P < 1      
     10      5      971.     974.843      0.015   0 < P < 1      
     10 Cohort df=  2                     0.488   P = 0.7833
     11      1       83.      75.617      0.721   0 < P < 1      
     11      2       56.      50.396      0.623   0 < P < 1      
     11      3      946.     958.987      0.176   0 < P < 1      
     11 Cohort df=  2                     1.520   P = 0.4677
     12      2      158.     145.427      1.087   0 < P < 1      
     12      3     1074.    1086.573      0.145   0 < P < 1      
     12 Cohort df=  1                     1.233   P = 0.2669
   ------------------------------------------------------------
@@    2  130    0  36   42.4007      24   42.0848     -126.955      277.910    
   G Total (Degrees of freedom =  36)      42.401
   Pr(Larger Chi-square) = 0.2144
   With pooling, Degrees of freedom =  24  Pearson Chi-square =     42.085
   Pr(Larger Chi-square) = 0.0126

   Log-likelihood = -126.95523        Akaike Information Criterion =  277.91045    

               PARAMETER     ESTIMATES FOR MODEL MODL_D    

                                                         95% Confidence Interval
   I       Parameter            S(I)     Standard Error    Lower         Upper
  ---  -------------------- ------------ ------------ ------------ ------------
   1   1 MOV(01,A,M) AA      0.698096     0.148408E-01 0.669008     0.727184    
   2   2 SRV(01,A,M) A       0.779541     0.176877E-01 0.744873     0.814209    
   3   3 MOV(01,A,M) BA      0.223989E-15 0.331077E-09 -.648912E-09 0.648912E-09
   4   4 SRV(01,A,M) B       0.778593     0.165709E-01 0.746114     0.811071    
   5   1 MOV(02,A,M) AA      0.698096     0.148408E-01 0.669008     0.727184    
   6   2 SRV(02,A,M) A       0.779541     0.176877E-01 0.744873     0.814209    
   7   3 MOV(02,A,M) BA      0.223989E-15 0.331077E-09 -.648912E-09 0.648912E-09
   8   4 SRV(02,A,M) B       0.778593     0.165709E-01 0.746114     0.811071    
   9   1 MOV(03,A,M) AA      0.698096     0.148408E-01 0.669008     0.727184    
  10   2 SRV(03,A,M) A       0.779541     0.176877E-01 0.744873     0.814209    
  11   3 MOV(03,A,M) BA      0.223989E-15 0.331077E-09 -.648912E-09 0.648912E-09
  12   4 SRV(03,A,M) B       0.778593     0.165709E-01 0.746114     0.811071    
  13   5 p(02,A,M) A         0.391556     0.196561E-01 0.353030     0.430082    
  14   6 p(02,A,M) B         0.386991     0.134749E-01 0.360580     0.413402    
  15   5 p(03,A,M) A         0.391556     0.196561E-01 0.353030     0.430082    
  16   6 p(03,A,M) B         0.386991     0.134749E-01 0.360580     0.413402    
  17   5 p(04,A,M) A         0.391556     0.196561E-01 0.353030     0.430082    
  18   6 p(04,A,M) B         0.386991     0.134749E-01 0.360580     0.413402    
  19   7 MOV(01,A,F) AA      0.613898     0.419646E-01 0.531647     0.696148    
  20   8 SRV(01,A,F) A       0.390622     0.272521E-01 0.337207     0.444036    
  21   9 MOV(01,A,F) BA      0.357247E-11 0.848155E-07 -.166235E-06 0.166242E-06
  22  10 SRV(01,A,F) B       0.383289     0.248185E-01 0.334644     0.431933    
  23   7 MOV(02,A,F) AA      0.613898     0.419646E-01 0.531647     0.696148    
  24   8 SRV(02,A,F) A       0.390622     0.272521E-01 0.337207     0.444036    
  25   9 MOV(02,A,F) BA      0.357247E-11 0.848155E-07 -.166235E-06 0.166242E-06
  26  10 SRV(02,A,F) B       0.383289     0.248185E-01 0.334644     0.431933    
  27   7 MOV(03,A,F) AA      0.613898     0.419646E-01 0.531647     0.696148    
  28   8 SRV(03,A,F) A       0.390622     0.272521E-01 0.337207     0.444036    
  29   9 MOV(03,A,F) BA      0.357247E-11 0.848155E-07 -.166235E-06 0.166242E-06
  30  10 SRV(03,A,F) B       0.383289     0.248185E-01 0.334644     0.431933    
  31  11 p(02,A,F) A         0.290629     0.408893E-01 0.210486     0.370772    
  32  12 p(02,A,F) B         0.307970     0.265552E-01 0.255922     0.360018    
  33  11 p(03,A,F) A         0.290629     0.408893E-01 0.210486     0.370772    
  34  12 p(03,A,F) B         0.307970     0.265552E-01 0.255922     0.360018    
  35  11 p(04,A,F) A         0.290629     0.408893E-01 0.210486     0.370772    
  36  12 p(04,A,F) B         0.307970     0.265552E-01 0.255922     0.360018    

     CPU time in seconds for last procedure was    1.56

  INPUT --- PROC ESTIMATE NOVAR NSIG=6 MAXFN=64000 NAME=MODL_B;
      Number of parameters in model  =  36

      Number of parameters set equal =  16

      Number of parameters fixed     =   0

      Number of parameters estimated =  20

     Final function value  11019.531     (Error Return = 130)

     Number of significant digits        3

     Number of function evaluations   1147

 * *  WARNING  * *   Rounding errors became dominant before parameters estimated

 * *  WARNING  * *   to NSIG digits for Model MODL_B    

 * *  WARNING  * *   Check to be sure the parameters are identifiable,

 * *  WARNING  * *   but the problem may just be ill-conditioned.

   Cohort  Cell   Observed  Expected  Chi-square  Note
   ------  ----   --------  --------  ----------  -------------
      1      1      236.     235.015      0.004   0 < P < 1      
      1      2      102.     101.021      0.009   0 < P < 1      
      1      3       76.      72.577      0.161   0 < P < 1      
      1      4       79.      75.912      0.126   0 < P < 1      
      1      5       22.      21.873      0.001   0 < P < 1      
      1      6       42.      41.662      0.003   0 < P < 1      
      1      7      443.     451.940      0.177   0 < P < 1      
      1 Cohort df=  6                     0.481   P = 0.9981
      2      2      338.     336.898      0.004   0 < P < 1      
      2      4      156.     149.009      0.328   0 < P < 1      
      2      6       64.      63.507      0.004   0 < P < 1      
      2      7      443.     451.586      0.163   0 < P < 1      
      2 Cohort df=  3                     0.499   P = 0.9192
      3      1      267.     270.924      0.057   0 < P < 1      
      3      2      114.     116.580      0.057   0 < P < 1      
      3      3       77.      81.651      0.265   0 < P < 1      
      3      4       80.      84.436      0.233   0 < P < 1      
      3      5      698.     682.409      0.356   0 < P < 1      
      3 Cohort df=  4                     0.968   P = 0.9146
      4      2      444.     452.505      0.160   0 < P < 1      
      4      4      183.     192.855      0.504   0 < P < 1      
      4      5      813.     794.640      0.424   0 < P < 1      
      4 Cohort df=  2                     1.088   P = 0.5805
      5      1      260.     255.726      0.071   0 < P < 1      
      5      2      111.     108.837      0.043   0 < P < 1      
      5      3      972.     978.437      0.042   0 < P < 1      
      5 Cohort df=  2                     0.157   P = 0.9246
      6      2      495.     484.098      0.246   0 < P < 1      
      6      3     1298.    1308.902      0.091   0 < P < 1      
      6 Cohort df=  1                     0.336   P = 0.5620
      7      1       62.      62.242      0.001   0 < P < 1      
      7      2       41.      41.537      0.007   0 < P < 1      
      7      3       11.      11.494      0.021   0 < P < 1      
      7      4       18.      19.590      0.129   0 < P < 1      
      7      5        2.       2.058      0.002   0 < P < 1      
      7      6        7.       6.882      0.002   0 < P < 1      
      7      7      859.     856.196      0.009   0 < P < 1      
      7 Cohort df=  6                     0.171   P = 0.9999
      8      2      105.     105.229      0.000   0 < P < 1      
      8      4       29.      30.287      0.055   0 < P < 1      
      8      6        8.       8.518      0.032   0 < P < 1      
      8      7      859.     856.965      0.005   0 < P < 1      
      8 Cohort df=  3                     0.092   P = 0.9928
      9      1       74.      73.260      0.007   0 < P < 1      
      9      2       50.      48.660      0.037   0 < P < 1      
      9      3       14.      13.116      0.060   0 < P < 1      
      9      4       23.      22.435      0.014   0 < P < 1      
      9      5      901.     904.530      0.014   0 < P < 1      
      9 Cohort df=  4                     0.132   P = 0.9979
     10      2      135.     132.891      0.033   0 < P < 1      
     10      4       40.      37.375      0.184   0 < P < 1      
     10      5      971.     975.734      0.023   0 < P < 1      
     10 Cohort df=  2                     0.241   P = 0.8866
     11      1       83.      83.808      0.008   0 < P < 1      
     11      2       56.      55.908      0.000   0 < P < 1      
     11      3      946.     945.284      0.001   0 < P < 1      
     11 Cohort df=  2                     0.008   P = 0.9958
     12      2      158.     160.665      0.044   0 < P < 1      
     12      3     1074.    1071.335      0.007   0 < P < 1      
     12 Cohort df=  1                     0.051   P = 0.8216
   ------------------------------------------------------------
@@    3  130    0  28   4.22760      16   4.22315     -107.869      255.737    
   G Total (Degrees of freedom =  28)       4.228
   Pr(Larger Chi-square) = 1.0000
   With pooling, Degrees of freedom =  16  Pearson Chi-square =      4.223
   Pr(Larger Chi-square) = 0.9985

   Log-likelihood = -107.86867        Akaike Information Criterion =  255.73734    

               PARAMETER     ESTIMATES FOR MODEL MODL_B    

                                                         95% Confidence Interval
   I       Parameter            S(I)     Standard Error    Lower         Upper
  ---  -------------------- ------------ ------------ ------------ ------------
   1   1 MOV(01,A,M) AA      0.699495     0.156129E-01 0.668893     0.730096    
   2   2 SRV(01,A,M) A       0.809333     0.194461E-01 0.771219     0.847447    
   3   3 MOV(01,A,M) BA      0.153274E-12 0.875236E-08 -.171545E-07 0.171548E-07
   4   4 SRV(01,A,M) B       0.810277     0.186997E-01 0.773626     0.846929    
   5   1 MOV(02,A,M) AA      0.699495     0.156129E-01 0.668893     0.730096    
   6   2 SRV(02,A,M) A       0.809333     0.194461E-01 0.771219     0.847447    
   7   3 MOV(02,A,M) BA      0.153274E-12 0.875236E-08 -.171545E-07 0.171548E-07
   8   4 SRV(02,A,M) B       0.810277     0.186997E-01 0.773626     0.846929    
   9   1 MOV(03,A,M) AA      0.699495     0.156129E-01 0.668893     0.730096    
  10   2 SRV(03,A,M) A       0.809333     0.194461E-01 0.771219     0.847447    
  11   3 MOV(03,A,M) BA      0.153274E-12 0.875236E-08 -.171545E-07 0.171548E-07
  12   4 SRV(03,A,M) B       0.810277     0.186997E-01 0.773626     0.846929    
  13   5 p(02,A,M) A         0.415130     0.255054E-01 0.365139     0.465121    
  14   6 p(02,A,M) B         0.415366     0.181679E-01 0.379757     0.450975    
  15   7 p(03,A,M) A         0.387183     0.243717E-01 0.339415     0.434952    
  16   8 p(03,A,M) B         0.387817     0.163238E-01 0.355823     0.419812    
  17   9 p(04,A,M) A         0.336347     0.247926E-01 0.287753     0.384940    
  18  10 p(04,A,M) B         0.333211     0.163182E-01 0.301228     0.365195    
  19  11 MOV(01,A,F) AA      0.612762     0.430408E-01 0.528403     0.697122    
  20  12 SRV(01,A,F) A       0.373504     0.269556E-01 0.320671     0.426337    
  21  13 MOV(01,A,F) BA      0.795825E-12 0.398934E-07 -.781903E-07 0.781919E-07
  22  14 SRV(01,A,F) B       0.366048     0.250264E-01 0.316996     0.415099    
  23  11 MOV(02,A,F) AA      0.612762     0.430408E-01 0.528403     0.697122    
  24  12 SRV(02,A,F) A       0.373504     0.269556E-01 0.320671     0.426337    
  25  13 MOV(02,A,F) BA      0.795825E-12 0.398934E-07 -.781903E-07 0.781919E-07
  26  14 SRV(02,A,F) B       0.366048     0.250264E-01 0.316996     0.415099    
  27  11 MOV(03,A,F) AA      0.612762     0.430408E-01 0.528403     0.697122    
  28  12 SRV(03,A,F) A       0.373504     0.269556E-01 0.320671     0.426337    
  29  13 MOV(03,A,F) BA      0.795825E-12 0.398934E-07 -.781903E-07 0.781919E-07
  30  14 SRV(03,A,F) B       0.366048     0.250264E-01 0.316996     0.415099    
  31  15 p(02,A,F) A         0.271953     0.438024E-01 0.186101     0.357806    
  32  16 p(02,A,F) B         0.287187     0.286197E-01 0.231093     0.343282    
  33  17 p(03,A,F) A         0.301408     0.495588E-01 0.204273     0.398543    
  34  18 p(03,A,F) B         0.316791     0.315622E-01 0.254929     0.378653    
  35  19 p(04,A,F) A         0.337494     0.593484E-01 0.221171     0.453817    
  36  20 p(04,A,F) B         0.356265     0.389534E-01 0.279916     0.432613    

     CPU time in seconds for last procedure was    2.22

  INPUT --- PROC ESTIMATE NOVAR NSIG=6 MAXFN=64000 NAME=MODL_A;
      Number of parameters in model  =  36

      Number of parameters set equal =   0

      Number of parameters fixed     =   4

      Number of parameters estimated =  32

     Final function value  11017.458     (Error Return = 130)

     Number of significant digits        5

     Number of function evaluations   2182

 * *  WARNING  * *   Rounding errors became dominant before parameters estimated

 * *  WARNING  * *   to NSIG digits for Model MODL_A    

 * *  WARNING  * *   Check to be sure the parameters are identifiable,

 * *  WARNING  * *   but the problem may just be ill-conditioned.

   Cohort  Cell   Observed  Expected  Chi-square  Note
   ------  ----   --------  --------  ----------  -------------
      1      1      236.     236.000      0.000   0 < P < 1      
      1      2      102.     101.823      0.000   0 < P < 1      
      1      3       76.      75.943      0.000   0 < P < 1      
      1      4       79.      79.281      0.001   0 < P < 1      
      1      5       22.      21.929      0.000   0 < P < 1      
      1      6       42.      42.024      0.000   0 < P < 1      
      1      7      443.     443.000      0.000   0 < P < 1      
      1 Cohort df=  6                     0.002   P = 1.0000
      2      2      338.     338.177      0.000   0 < P < 1      
      2      4      156.     155.691      0.001   0 < P < 1      
      2      6       64.      64.131      0.000   0 < P < 1      
      2      7      443.     443.000      0.000   0 < P < 1      
      2 Cohort df=  3                     0.001   P = 1.0000
      3      1      267.     267.057      0.000   0 < P < 1      
      3      2      114.     113.949      0.000   0 < P < 1      
      3      3       77.      77.116      0.000   0 < P < 1      
      3      4       80.      79.878      0.000   0 < P < 1      
      3      5      698.     698.000      0.000   0 < P < 1      
      3 Cohort df=  4                     0.000   P = 1.0000
      4      2      444.     444.079      0.000   0 < P < 1      
      4      4      183.     182.921      0.000   0 < P < 1      
      4      5      813.     813.000      0.000   0 < P < 1      
      4 Cohort df=  2                     0.000   P = 1.0000
      5      1      260.     259.955      0.000   0 < P < 1      
      5      2      111.     111.045      0.000   0 < P < 1      
      5      3      972.     972.000      0.000   0 < P < 1      
      5 Cohort df=  2                     0.000   P = 1.0000
      6      2      495.     495.000      0.000   0 < P < 1      
      6      3     1298.    1298.000      0.000   0 < P < 1      
      6 Cohort df=  1                     0.000   P = 1.0000
      7      1       62.      62.000      0.000   0 < P < 1      
      7      2       41.      40.877      0.000   0 < P < 1      
      7      3       11.      10.940      0.000   0 < P < 1      
      7      4       18.      18.418      0.010   0 < P < 1      
      7      5        2.       2.033      0.001   0 < P < 1      
      7      6        7.       6.731      0.011   0 < P < 1      
      7      7      859.     859.000      0.000   0 < P < 1      
      7 Cohort df=  6                     0.021   P = 1.0000
      8      2      105.     105.123      0.000   0 < P < 1      
      8      4       29.      28.555      0.007   0 < P < 1      
      8      6        8.       8.322      0.012   0 < P < 1      
      8      7      859.     859.000      0.000   0 < P < 1      
      8 Cohort df=  3                     0.019   P = 0.9993
      9      1       74.      74.060      0.000   0 < P < 1      
      9      2       50.      49.516      0.005   0 < P < 1      
      9      3       14.      13.764      0.004   0 < P < 1      
      9      4       23.      23.660      0.018   0 < P < 1      
      9      5      901.     901.000      0.000   0 < P < 1      
      9 Cohort df=  4                     0.027   P = 0.9999
     10      2      135.     135.510      0.002   0 < P < 1      
     10      4       40.      39.490      0.007   0 < P < 1      
     10      5      971.     971.000      0.000   0 < P < 1      
     10 Cohort df=  2                     0.008   P = 0.9958
     11      1       83.      83.203      0.000   0 < P < 1      
     11      2       56.      55.797      0.001   0 < P < 1      
     11      3      946.     946.000      0.000   0 < P < 1      
     11 Cohort df=  2                     0.001   P = 0.9994
     12      2      158.     158.000      0.000   0 < P < 1      
     12      3     1074.    1074.000      0.000   0 < P < 1      
     12 Cohort df=  1                     0.000   P = 1.0000
   ------------------------------------------------------------
@@    4  130    0  16  0.811741E-01   4  0.810022E-01 -105.795      275.591    
   G Total (Degrees of freedom =  16)       0.081
   Pr(Larger Chi-square) = 1.0000
   With pooling, Degrees of freedom =   4  Pearson Chi-square =      0.081
   Pr(Larger Chi-square) = 0.9992

   Log-likelihood = -105.79546        Akaike Information Criterion =  275.59091    

               PARAMETER     ESTIMATES FOR MODEL MODL_A    

                                                         95% Confidence Interval
   I       Parameter            S(I)     Standard Error    Lower         Upper
  ---  -------------------- ------------ ------------ ------------ ------------
   1   1 MOV(01,A,M) AA      0.698291     0.272011E-01 0.644977     0.751605    
   2   2 SRV(01,A,M) A       0.841311     0.301219E-01 0.782272     0.900350    
   3   3 MOV(01,A,M) BA      0.791250E-13 0.152194E-07 -.298299E-07 0.298300E-07
   4   4 SRV(01,A,M) B       0.842191     0.313906E-01 0.780665     0.903717    
   5   5 MOV(02,A,M) AA      0.700908     0.263021E-01 0.649355     0.752460    
   6   6 SRV(02,A,M) A       0.768141     0.344931E-01 0.700534     0.835747    
   7   7 MOV(02,A,M) BA      0.161038E-11 0.505247E-07 -.990267E-07 0.990300E-07
   8   8 SRV(02,A,M) B       0.768514     0.332930E-01 0.703260     0.833769    
   9   9 MOV(03,A,M) AA      0.700688     0.224495E-01 0.656687     0.744689    
  10  10 SRV(03,A,M) A       0.276247     0.122013E-01 0.252333     0.300162    
  11  11 MOV(03,A,M) BA      0.267271E-11 0.639044E-07 -.125250E-06 0.125255E-06
  12  12 SRV(03,A,M) B       0.276074     0.105577E-01 0.255381     0.296767    
  13  13 p(02,A,M) A         0.401716     0.288422E-01 0.345185     0.458247    
  14  14 p(02,A,M) B         0.401144     0.206752E-01 0.360620     0.441667    
  15  15 p(03,A,M) A         0.401314     0.289046E-01 0.344661     0.457967    
  16  16 p(03,A,M) B         0.401278     0.190077E-01 0.364023     0.438533    
  17 -33 p(04,A,M) A          1.00000     0.000000E+00  1.00000      1.00000    
  18 -34 p(04,A,M) B          1.00000     0.000000E+00  1.00000      1.00000    
  19  19 MOV(01,A,F) AA      0.618899     0.707288E-01 0.480270     0.757527    
  20  20 SRV(01,A,F) A       0.353662     0.409073E-01 0.273484     0.433841    
  21  21 MOV(01,A,F) BA      0.181829E-15 0.134831E-08 -.264270E-08 0.264270E-08
  22  22 SRV(01,A,F) B       0.346269     0.414183E-01 0.265089     0.427449    
  23  23 MOV(02,A,F) AA      0.610099     0.647022E-01 0.483283     0.736916    
  24  24 SRV(02,A,F) A       0.391317     0.437016E-01 0.305662     0.476972    
  25  25 MOV(02,A,F) BA      0.883231E-15 0.231888E-08 -.454501E-08 0.454501E-08
  26  26 SRV(02,A,F) B       0.386940     0.429353E-01 0.302787     0.471094    
  27  27 MOV(03,A,F) AA      0.598583     0.402479E-01 0.519697     0.677469    
  28  28 SRV(03,A,F) A       0.128111     0.101463E-01 0.108224     0.147997    
  29  29 MOV(03,A,F) BA      0.658437E-15 0.190194E-08 -.372781E-08 0.372781E-08
  30  30 SRV(03,A,F) B       0.128247     0.952609E-02 0.109576     0.146918    
  31  31 p(02,A,F) A         0.283259     0.590986E-01 0.167425     0.399092    
  32  32 p(02,A,F) B         0.303285     0.399842E-01 0.224915     0.381654    
  33  17 p(03,A,F) A         0.292098     0.563421E-01 0.181667     0.402528    
  34  18 p(03,A,F) B         0.305592     0.351321E-01 0.236733     0.374451    
  35 -35 p(04,A,F) A          1.00000     0.000000E+00  1.00000      1.00000    
  36 -36 p(04,A,F) B          1.00000     0.000000E+00  1.00000      1.00000    

     CPU time in seconds for last procedure was    4.20

  INPUT --- PROC ESTIMATE NOVAR NSIG=6 MAXFN=64000 NAME=1GRP_A;
      Number of parameters in model  =  36

      Number of parameters set equal =  16

      Number of parameters fixed     =   4

      Number of parameters estimated =  16

     Final function value  11767.052     (Error Return = 130)

     Number of significant digits        5

     Number of function evaluations    946

 * *  WARNING  * *   Rounding errors became dominant before parameters estimated

 * *  WARNING  * *   to NSIG digits for Model 1GRP_A    

 * *  WARNING  * *   Check to be sure the parameters are identifiable,

 * *  WARNING  * *   but the problem may just be ill-conditioned.

   Cohort  Cell   Observed  Expected  Chi-square  Note
   ------  ----   --------  --------  ----------  -------------
      1      1      236.     149.000     50.799   0 < P < 1      
      1      2      102.      70.658     13.902   0 < P < 1      
      1      3       76.      43.346     24.599   0 < P < 1      
      1      4       79.      49.802     17.119   0 < P < 1      
      1      5       22.      11.529      9.510   0 < P < 1      
      1      6       42.      24.665     12.183   0 < P < 1      
      1      7      443.     651.000     66.458   0 < P < 1      
      1 Cohort df=  6                   194.570   P = 0.0000
      2      2      338.     222.342     60.164   0 < P < 1      
      2      4      156.      92.258     44.041   0 < P < 1      
      2      6       64.      35.401     23.104   0 < P < 1      
      2      7      443.     651.000     66.458   0 < P < 1      
      2 Cohort df=  3                   193.766   P = 0.0000
      3      1      267.     183.576     37.912   0 < P < 1      
      3      2      114.      86.748      8.561   0 < P < 1      
      3      3       77.      48.826     16.257   0 < P < 1      
      3      4       80.      56.814      9.462   0 < P < 1      
      3      5      698.     860.037     30.529   0 < P < 1      
      3 Cohort df=  4                   102.721   P = 0.0000
      4      2      444.     322.746     45.554   0 < P < 1      
      4      4      183.     123.843     28.258   0 < P < 1      
      4      5      813.     993.411     32.764   0 < P < 1      
      4 Cohort df=  2                   106.576   P = 0.0000
      5      1      260.     190.367     25.470   0 < P < 1      
      5      2      111.      91.729      4.048   0 < P < 1      
      5      3      972.    1060.904      7.450   0 < P < 1      
      5 Cohort df=  2                    36.969   P = 0.0000
      6      2      495.     387.051     30.107   0 < P < 1      
      6      3     1298.    1405.949      8.288   0 < P < 1      
      6 Cohort df=  1                    38.396   P = 0.0000
      7      1       62.     149.000     50.799   0 < P < 1      
      7      2       41.      70.658     12.449   0 < P < 1      
      7      3       11.      43.346     24.137   0 < P < 1      
      7      4       18.      49.802     20.307   0 < P < 1      
      7      5        2.      11.529      7.876   0 < P < 1      
      7      6        7.      24.665     12.652   0 < P < 1      
      7      7      859.     651.000     66.458   0 < P < 1      
      7 Cohort df=  6                   194.678   P = 0.0000
      8      2      105.     222.342     61.927   0 < P < 1      
      8      4       29.      92.258     43.373   0 < P < 1      
      8      6        8.      35.401     21.209   0 < P < 1      
      8      7      859.     651.000     66.458   0 < P < 1      
      8 Cohort df=  3                   192.967   P = 0.0000
      9      1       74.     157.732     44.449   0 < P < 1      
      9      2       50.      74.536      8.077   0 < P < 1      
      9      3       14.      41.953     18.625   0 < P < 1      
      9      4       23.      48.816     13.652   0 < P < 1      
      9      5      901.     738.963     35.531   0 < P < 1      
      9 Cohort df=  4                   120.334   P = 0.0000
     10      2      135.     256.852     57.807   0 < P < 1      
     10      4       40.      98.559     34.793   0 < P < 1      
     10      5      971.     790.589     41.169   0 < P < 1      
     10 Cohort df=  2                   133.769   P = 0.0000
     11      1       83.     153.796     32.589   0 < P < 1      
     11      2       56.      74.107      4.424   0 < P < 1      
     11      3      946.     857.096      9.222   0 < P < 1      
     11 Cohort df=  2                    46.235   P = 0.0000
     12      2      158.     265.949     43.817   0 < P < 1      
     12      3     1074.     966.051     12.063   0 < P < 1      
     12 Cohort df=  1                    55.879   P = 0.0000
   ------------------------------------------------------------
@@    5  130    0  32   1499.27      20   1416.86     -855.390      1742.78    
   G Total (Degrees of freedom =  32)    1499.270
   Pr(Larger Chi-square) = 0.0000
   With pooling, Degrees of freedom =  20  Pearson Chi-square =   1416.861
   Pr(Larger Chi-square) = 0.0000

   Log-likelihood = -855.38982        Akaike Information Criterion =  1742.7796    

               PARAMETER     ESTIMATES FOR MODEL 1GRP_A    

                                                         95% Confidence Interval
   I       Parameter            S(I)     Standard Error    Lower         Upper
  ---  -------------------- ------------ ------------ ------------ ------------
   1   1 MOV(01,A,M) AA      0.686338     0.259820E-01 0.635413     0.737262    
   2   2 SRV(01,A,M) A       0.642315     0.258643E-01 0.591621     0.693009    
   3   3 MOV(01,A,M) BA      0.424835E-17 0.995660E-10 -.195149E-09 0.195149E-09
   4   4 SRV(01,A,M) B       0.633335     0.262895E-01 0.581808     0.684862    
   5   5 MOV(02,A,M) AA      0.686668     0.248164E-01 0.638027     0.735308    
   6   6 SRV(02,A,M) A       0.622153     0.280548E-01 0.567166     0.677141    
   7   7 MOV(02,A,M) BA      0.308311E-12 0.204126E-07 -.400083E-07 0.400089E-07
   8   8 SRV(02,A,M) B       0.622532     0.269198E-01 0.569769     0.675295    
   9   9 MOV(03,A,M) AA      0.674830     0.196852E-01 0.636247     0.713413    
  10  10 SRV(03,A,M) A       0.210049     0.826678E-02 0.193847     0.226252    
  11  11 MOV(03,A,M) BA      0.133071E-10 0.118946E-06 -.233120E-06 0.233147E-06
  12  12 SRV(03,A,M) B       0.215868     0.748042E-02 0.201206     0.230529    
  13  13 p(02,A,M) A         0.337987     0.248288E-01 0.289323     0.386652    
  14  14 p(02,A,M) B         0.350714     0.179123E-01 0.315606     0.385822    
  15  15 p(03,A,M) A         0.347658     0.249419E-01 0.298772     0.396544    
  16  16 p(03,A,M) B         0.360028     0.165166E-01 0.327656     0.392401    
  17 -33 p(04,A,M) A          1.00000     0.000000E+00  1.00000      1.00000    
  18 -34 p(04,A,M) B          1.00000     0.000000E+00  1.00000      1.00000    
  19   1 MOV(01,A,F) AA      0.686338     0.259820E-01 0.635413     0.737262    
  20   2 SRV(01,A,F) A       0.642315     0.258643E-01 0.591621     0.693009    
  21   3 MOV(01,A,F) BA      0.424835E-17 0.995660E-10 -.195149E-09 0.195149E-09
  22   4 SRV(01,A,F) B       0.633335     0.262895E-01 0.581808     0.684862    
  23   5 MOV(02,A,F) AA      0.686668     0.248164E-01 0.638027     0.735308    
  24   6 SRV(02,A,F) A       0.622153     0.280548E-01 0.567166     0.677141    
  25   7 MOV(02,A,F) BA      0.308311E-12 0.204126E-07 -.400083E-07 0.400089E-07
  26   8 SRV(02,A,F) B       0.622532     0.269198E-01 0.569769     0.675295    
  27   9 MOV(03,A,F) AA      0.674830     0.196852E-01 0.636247     0.713413    
  28  10 SRV(03,A,F) A       0.210049     0.826678E-02 0.193847     0.226252    
  29  11 MOV(03,A,F) BA      0.133071E-10 0.118946E-06 -.233120E-06 0.233147E-06
  30  12 SRV(03,A,F) B       0.215868     0.748042E-02 0.201206     0.230529    
  31  13 p(02,A,F) A         0.337987     0.248288E-01 0.289323     0.386652    
  32  14 p(02,A,F) B         0.350714     0.179123E-01 0.315606     0.385822    
  33  15 p(03,A,F) A         0.347658     0.249419E-01 0.298772     0.396544    
  34  16 p(03,A,F) B         0.360028     0.165166E-01 0.327656     0.392401    
  35 -35 p(04,A,F) A          1.00000     0.000000E+00  1.00000      1.00000    
  36 -36 p(04,A,F) B          1.00000     0.000000E+00  1.00000      1.00000    

     CPU time in seconds for last procedure was    1.77

  INPUT --- PROC TEST;

 Submodel    Name               Log-likelihood  NDF  Akaike Inf. Criter.   G-O-F
 --------  -------------------  --------------  ---  -------------------  ------
     3     MODL_B                -107.869       28      255.73734        1.0000
     1     ULTRA1/*              -105.812       22      263.62421        1.0000
     4     MODL_A                -105.795       16      275.59091        1.0000
     2     MODL_D                -126.955       36      277.91045        0.0000
     5     1GRP_A                -855.390       32      1742.7796        0.0000

                     Likelihood Ratio Tests Between Models
  General              Reduced                           Degrees   Pr(Larger 
  Submodel             Submodel              Chi-square  Freedom  Chi-square)
 ----------           ----------             ----------  -------  -----------
 ULTRA1/*              MODL_B                     4.113      6       0.6614
 MODL_A                MODL_B                     4.146     12       0.9806
 MODL_B                MODL_D                    38.173      8       0.0000
 MODL_B                1GRP_A                  1495.042      4       0.0000
 MODL_A                ULTRA1/*                   0.033      6       1.0000
 ULTRA1/*              MODL_D                    42.286     14       0.0001
 ULTRA1/*              1GRP_A                  1499.155     10       0.0000
 MODL_A                MODL_D                    42.320     20       0.0025
 MODL_A                1GRP_A                  1499.189     16       0.0000
 1GRP_A                MODL_D                     0.000      4       1.0000

 * *  WARNING  * *   Sequence of models reinitialized to zero.
     CPU time in seconds for last procedure was    0.00
  INPUT --- PROC STOP;
     CPU time in minutes for this job was    0.30
          E X E C U T I O N   S U C C E S S F U L 

User-defined models

After running CNVMEMOV, other models may be added to the ones produced by default. To add new models, edit the CNVMEMOV output file, CNVMEMOV.OUT with a text editor. If a word-processor (eg. Word, Word Perfect, WordPro,...) is used, the file must be saved in ASCII or DOS text format.

Each model must begin with a ‘PROC ESTIMATE' statement. This is followed by ‘INITIAL', and ‘CONSTRAINTS' statements. The statements following the ‘CONSTRAINTS;' statement define how the parameters are related to each other. The best procedure for designing a model is to copy the statements from a previous model and modify the copy. For example, to build a model where survival/movement is time-specific and capture-probabilities are constant over time, you could copy the statements from model ‘D' and delete the statements which constrain survival/transition parameters.

The following rules must be followed when constraining parameters:

1) Parameters can be constrained to be less than, greater than, or equal to constant values. (Eg. S(10)=1; S(11)<0.5; S(12)>0.1;) 2) Parameters can not be constrained to be less than or greater than other parameters. (Eg. S(10)>S(11) - invalid) 3) Parameters can not be constrained to be equal to a previously constrained parameter. (Eg. S(5)=S(1); S(10)=S(5); - invalid S(5)=S(1); S(10)=S(1); - valid)

PROC ESTIMATE NOVAR NSIG=6 MAXFN=64000 NAME=MODL_C;
INITIAL; ALL= 0.500;
CONSTRAINTS;
S(015)=S(013) /* p(03,A,M) A   =p(02,A,M) A    */;
S(016)=S(014) /* p(03,A,M) B   =p(02,A,M) B    */;
S(017)=S(013) /* p(04,A,M) A   =p(02,A,M) A    */;
S(018)=S(014) /* p(04,A,M) B   =p(02,A,M) B    */;
S(033)=S(031) /* p(03,A,F) A   =p(02,A,F) A    */;
S(034)=S(032) /* p(03,A,F) B   =p(02,A,F) B    */;
S(035)=S(031) /* p(04,A,F) A   =p(02,A,F) A    */;
S(036)=S(032) /* p(04,A,F) B   =p(02,A,F) B    */;

External Covariates and additive models

To define models with external covariates a few new statements are needed. The list of parameters can be mapped to a new set of parameters using the ‘PIM' and ‘DESMAT' statements. The ‘PIM' (Parameter Information Matrix) statement is used to map the actual parameters to unique transformed parameters. The unique transformed parameters are multiplied by the design matrix to give the value for the actual parameter. For example, to model survival and transition probabilities and capture probabilities as constant over time (as in model D), the PIM would be:

PIM;
1 2 3 4 1 2 3 4 1 2 3 4 5 6 5 6 5 6 7 8 9 10 7 8 9 10 7 8 9 10 11 12 11 12 11 12;

These 2 statements cause parameters 1,5,9 {mov(*,a,m) AA} to be mapped to a new parameter 1. This parameter would be the probability of moving from strata A to A for the first group(m) for any of the time-periods. Similarly, parameters 2,6,10 would be mapped to a new parameter 2. Using these two statements gives the same results as using the constraints in model D.

Although this statement could be used to generate models, the intended purpose of the PIM statement is to help generate additive or covariate models. Additive models are models where one parameter is defined in terms of other parameter(s) plus fixed values. Covariate models are models where parameters are defined as a function of some external variable (eg. Rainfall, temperature). For example, if we wanted to define a model where survival for groups M and F are related to an external covariate (temperature), the PIM would be:

PIM;
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
 24 25 26 27 28 29 30 31 32 33 34 35 36;

In this example, each parameter is mapped to a transformed parameter. The transformed parameters are computed by multiplying the design matrix by the estimable parameters. The default design matrix is the identity matrix (zeros except on the diagonal; ones on the diagonal). This matrix would yield no transformation of the parameters. The transformation of parameters is achieved by matrix multiplication of the design matrix and the parameter vector. Here is an example where there are 4 parameters(p1-p4) , and the last two are equal to the first two plus a constant (t3)

[P1]= [1 0 0] [  ] , [T1]
[P2]= [0 1 0] [T1] , [T2]
[P3]= [1 0 1] [T2] , [T1+T3]
[P4]= [0 1 1] [T3] , [T2+T3]
In the previous example, the design matrix contains only ones and zeros. To specify that the parameters are to be a function of an external variable, the external variable can be inserted into a column of the design matrix. In the following example, only one parameter will be estimated, t1, and the actual parameters, p1-p4 will be computed using t1 and the covariates (.44 .48 .41 .52).

[P1]= [.44]      , [.44T1]
[P2]= [.48] [T1] , [.48T1]
[P3]= [.41]      , [.41T1]
[P4]= [.52]      , [.52T1]

Here is the input for generating a model where survival for the 2 groups are a function of an external variable and capture and movement probabilities vary over time and group:

PROC ESTIMATE NOVAR NSIG=6 MAXFN=64000 NAME=ULTRA1
/* SRV(M) = F(A1,X), SRV(F)=F(A2,X) */;
LABELS;
S(1)=MOV(01,A,M) AA ;
S(2)=MOV(01,A,M) BA ;
S(3)=MOV(02,A,M) AA ;
S(4)=MOV(02,A,M) BA ;
S(5)=MOV(03,A,M) AA ;
S(6)=MOV(03,A,M) BA ;
S(7)=p(02,A,M) A ;
S(8)=p(02,A,M) B ;
S(9)=p(03,A,M) A ;
S(10)=p(03,A,M) B ;
S(11)=p(04,A,M) A ;
S(12)=p(04,A,M) B ;
S(13)=MOV(01,A,F) AA ;
S(14)=MOV(01,A,F) BA ;
S(15)=MOV(02,A,F) AA ;
S(16)=MOV(02,A,F) BA ;
S(17)=MOV(03,A,F) AA ;
S(18)=MOV(03,A,F) BA ;
S(19)=p(02,A,F) A ;
S(20)=p(02,A,F) B ;
S(21)=p(03,A,F) A ;
S(22)=p(03,A,F) B ;
S(23)=p(04,A,F) A ;
S(24)=p(04,A,F) B ;
S(25)=A1 ;
S(26)=A2 ;
PIM;
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36;
DESMAT 36 26;
SUBMAT 1 1 TO 36 26;
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .21 0;
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .21 0;
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .15 0;
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .15 0;
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .10 0;
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .10 0;
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0;
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0;
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0;
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0;
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0;
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0   0;
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0   0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .21;
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0   0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .21;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0   0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .15;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0   0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .15;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0   0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .10;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0   0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .10;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0   0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0   0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0   0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0   0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0   0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0   0;
INITIAL; ALL= 0.500;

First, notice the comment in the PROC ESTIMATE which is enclosed by /* and */. Since the parameters are transformed, new definitions of the transformed parameters would be helpful in reading the output (LABELS;). The PIM statement specifies that all 36 parameters are unique. The DESMAT statement declares the size of the matrix to be 36 rows by 26 columns. Each row of the design matrix corresponds to one of the 36 original parameters, and each column corresponds to one of the 26 transformed parameters.

To make defining the design matrix easier, you only need specify parts of the matrix which are different from the identity matrix. For clarity, the entire matrix is listed here, but it is possible to only specify a subset of the matrix using the SUBMAT statement. The 4 numbers of the SUBMAT statement specify the starting row and column followed by the ending row and column of values which follow.

The output produced by MSSURVIV for the previous model is:

  INPUT --- PROC ESTIMATE NOVAR NSIG=6 MAXFN=64000 NAME=ULTRA1/* SRV(M) 
  INPUT --- = F(A1,X), SRV(F)=F(A2,X) */;
      Number of parameters in model  =  36

      Number of parameters set equal =   0

      Number of parameters fixed     =   0

      Number of parameters estimated =  26

     Final function value  11017.474     (Error Return = 130)

     Number of significant digits        5

     Number of function evaluations   2514

 * *  WARNING  * *   Rounding errors became dominant before parameters estimated

 * *  WARNING  * *   to NSIG digits for Model ULTRA1/*  

 * *  WARNING  * *   Check to be sure the parameters are identifiable,

 * *  WARNING  * *   but the problem may just be ill-conditioned.

   Cohort  Cell   Observed  Expected  Chi-square  Note
   ------  ----   --------  --------  ----------  -------------
      1      1      236.     236.034      0.000   0 < P < 1      
      1      2      102.     101.866      0.000   0 < P < 1      
      1      3       76.      76.062      0.000   0 < P < 1      
      1      4       79.      79.362      0.002   0 < P < 1      
      1      5       22.      21.968      0.000   0 < P < 1      
      1      6       42.      42.052      0.000   0 < P < 1      
      1      7      443.     442.656      0.000   0 < P < 1      
      1 Cohort df=  6                     0.002   P = 1.0000
      2      2      338.     338.131      0.000   0 < P < 1      
      2      4      156.     155.669      0.001   0 < P < 1      
      2      6       64.      64.076      0.000   0 < P < 1      
      2      7      443.     443.124      0.000   0 < P < 1      
      2 Cohort df=  3                     0.001   P = 1.0000
      3      1      267.     266.950      0.000   0 < P < 1      
      3      2      114.     113.940      0.000   0 < P < 1      
      3      3       77.      77.098      0.000   0 < P < 1      
      3      4       80.      79.839      0.000   0 < P < 1      
      3      5      698.     698.173      0.000   0 < P < 1      
      3 Cohort df=  4                     0.001   P = 1.0000
      4      2      444.     443.987      0.000   0 < P < 1      
      4      4      183.     182.751      0.000   0 < P < 1      
      4      5      813.     813.262      0.000   0 < P < 1      
      4 Cohort df=  2                     0.000   P = 0.9998
      5      1      260.     259.938      0.000   0 < P < 1      
      5      2      111.     111.056      0.000   0 < P < 1      
      5      3      972.     972.006      0.000   0 < P < 1      
      5 Cohort df=  2                     0.000   P = 1.0000
      6      2      495.     495.210      0.000   0 < P < 1      
      6      3     1298.    1297.790      0.000   0 < P < 1      
      6 Cohort df=  1                     0.000   P = 0.9911
      7      1       62.      61.866      0.000   0 < P < 1      
      7      2       41.      40.652      0.003   0 < P < 1      
      7      3       11.      10.654      0.011   0 < P < 1      
      7      4       18.      18.216      0.003   0 < P < 1      
      7      5        2.       1.956      0.001   0 < P < 1      
      7      6        7.       6.662      0.017   0 < P < 1      
      7      7      859.     859.994      0.001   0 < P < 1      
      7 Cohort df=  5                     0.035   P = 1.0000
      8      2      105.     105.438      0.002   0 < P < 1      
      8      4       29.      28.856      0.001   0 < P < 1      
      8      6        8.       8.481      0.027   0 < P < 1      
      8      7      859.     858.225      0.001   0 < P < 1      
      8 Cohort df=  3                     0.031   P = 0.9986
      9      1       74.      74.262      0.001   0 < P < 1      
      9      2       50.      49.421      0.007   0 < P < 1      
      9      3       14.      13.630      0.010   0 < P < 1      
      9      4       23.      23.646      0.018   0 < P < 1      
      9      5      901.     901.040      0.000   0 < P < 1      
      9 Cohort df=  4                     0.035   P = 0.9998
     10      2      135.     135.649      0.003   0 < P < 1      
     10      4       40.      39.868      0.000   0 < P < 1      
     10      5      971.     970.483      0.000   0 < P < 1      
     10 Cohort df=  2                     0.004   P = 0.9981
     11      1       83.      83.399      0.002   0 < P < 1      
     11      2       56.      55.807      0.001   0 < P < 1      
     11      3      946.     945.794      0.000   0 < P < 1      
     11 Cohort df=  2                     0.003   P = 0.9987
     12      2      158.     157.567      0.001   0 < P < 1      
     12      3     1074.    1074.433      0.000   0 < P < 1      
     12 Cohort df=  1                     0.001   P = 0.9705
   ------------------------------------------------------------
@@    1  130    0  22  0.114473       9  0.113113     -105.812      263.624    
   G Total (Degrees of freedom =  22)       0.114
   Pr(Larger Chi-square) = 1.0000
   With pooling, Degrees of freedom =   9  Pearson Chi-square =      0.113
   Pr(Larger Chi-square) = 1.0000

   Log-likelihood = -105.81211        Akaike Information Criterion =  263.62421    
         itrans,nyrs=     2    4

 SURVIVAL/MOVEMENT & CAPTURE PROB. ESTIMATES
    1 MOV(01,A,M) AA            0.698437    
    2 SRV(01,A,M) A             0.842177    
    3 MOV(01,A,M) BA            0.565833E-12
    4 SRV(01,A,M) B             0.842177    
    5 MOV(02,A,M) AA            0.701015    
    6 SRV(02,A,M) A             0.767827    
    7 MOV(02,A,M) BA            0.103410E-10
    8 SRV(02,A,M) B             0.767827    
    9 MOV(03,A,M) AA            0.700596    
   10 SRV(03,A,M) A             0.689415    
   11 MOV(03,A,M) BA            0.861494E-15
   12 SRV(03,A,M) B             0.689415    
   13 p(02,A,M) A               0.401277    
   14 p(02,A,M) B               0.401096    
   15 p(03,A,M) A               0.401256    
   16 p(03,A,M) B               0.401554    
   17 p(04,A,M) A               0.400724    
   18 p(04,A,M) B               0.400616    
   19 MOV(01,A,F) AA            0.614067    
   20 SRV(01,A,F) A             0.348870    
   21 MOV(01,A,F) BA            0.548536E-45
   22 SRV(01,A,F) B             0.348870    
   23 MOV(02,A,F) AA            0.606850    
   24 SRV(02,A,F) A             0.390379    
   25 MOV(02,A,F) BA            0.521048E-29
   26 SRV(02,A,F) B             0.390379    
   27 MOV(03,A,F) AA            0.597835    
   28 SRV(03,A,F) A             0.426255    
   29 MOV(03,A,F) BA            0.422671E-11
   30 SRV(03,A,F) B             0.426255    
   31 p(02,A,F) A               0.288786    
   32 p(02,A,F) B               0.301926    
   33 p(03,A,F) A               0.295174    
   34 p(03,A,F) B               0.303211    
   35 p(04,A,F) A               0.301634    
   36 p(04,A,F) B               0.300044    

               UNTRANSFORMED ESTIMATES FOR MODEL ULTRA1/*  

                                                         95% Confidence Interval
   I       Parameter            S(I)     Standard Error    Lower         Upper
  ---  -------------------- ------------ ------------ ------------ ------------
   1   1 MOV(01,A,M) AA      0.839867     0.528164E-01 0.736346     0.943387    
   2   2 MOV(01,A,M) BA      -20.0000     0.427416E-01 -20.0838     -19.9162    
   3   3 MOV(02,A,M) AA      0.852135     0.472473E-01 0.759530     0.944739    
   4   4 MOV(02,A,M) BA      -20.0000     0.349412E-01 -20.0685     -19.9315    
   5   5 MOV(03,A,M) AA      0.850136     0.522983E-01 0.747631     0.952640    
   6   6 MOV(03,A,M) BA      -20.0000     0.354779E-01 -20.0695     -19.9305    
   7   7 p(02,A,M) A         -.400146     0.361840E-01 -.471066     -.329225    
   8   8 p(02,A,M) B         -.400902     0.330581E-01 -.465696     -.336109    
   9   9 p(03,A,M) A         -.400235     0.325735E-01 -.464080     -.336391    
  10  10 p(03,A,M) B         -.398993     0.290952E-01 -.456019     -.341966    
  11  11 p(04,A,M) A         -.402450     0.505944E-01 -.501615     -.303285    
  12  12 p(04,A,M) B         -.402898     0.476067E-01 -.496207     -.309589    
  13  13 MOV(01,A,F) AA      0.464440     0.240815     -.755734E-02 0.936438    
  14  14 MOV(01,A,F) BA      -20.0000     0.178446     -20.3498     -19.6502    
  15  15 MOV(02,A,F) AA      0.434089     0.193629     0.545757E-01 0.813603    
  16  16 MOV(02,A,F) BA      -20.0000     0.132460     -20.2596     -19.7404    
  17  17 MOV(03,A,F) AA      0.396454     0.192605     0.189479E-01 0.773960    
  18  18 MOV(03,A,F) BA      -20.0000     0.114655     -20.2247     -19.7753    
  19  19 p(02,A,F) A         -.901288     0.113968     -1.12467     -.677910    
  20  20 p(02,A,F) B         -.838141     0.973045E-01 -1.02886     -.647424    
  21  21 p(03,A,F) A         -.870388     0.902454E-01 -1.04727     -.693507    
  22  22 p(03,A,F) B         -.832054     0.737722E-01 -.976647     -.687460    
  23  23 p(04,A,F) A         -.839531     0.818452E-01 -.999948     -.679114    
  24  24 p(04,A,F) B         -.847088     0.587391E-01 -.962217     -.731959    
  25  25 A1                   7.97388      1.13913      5.74118      10.2066    
  26  26 A2                  -2.97148     0.408431     -3.77200     -2.17095    

               PARAMETER     ESTIMATES FOR MODEL ULTRA1/*  

                                                         95% Confidence Interval
   I       Parameter            S(I)     Standard Error    Lower         Upper
  ---  -------------------- ------------ ------------ ------------ ------------
   1   1 MOV(01,A,M) AA      0.698437     0.111245E-01 0.676633     0.720241    
   2   2 SRV(01,A,M) A       0.842177     0.317975E-01 0.779854     0.904500    
   3   3 MOV(01,A,M) BA      0.206115E-08 0.881853E-10 0.188831E-08 0.223400E-08
   4   4 SRV(01,A,M) B       0.842177     0.317975E-01 0.779854     0.904500    
   5   5 MOV(02,A,M) AA      0.701015     0.990287E-02 0.681605     0.720424    
   6   6 SRV(02,A,M) A       0.767827     0.304617E-01 0.708122     0.827532    
   7   7 MOV(02,A,M) BA      0.206115E-08 0.720913E-10 0.191985E-08 0.220245E-08
   8   8 SRV(02,A,M) B       0.767827     0.304617E-01 0.708122     0.827532    
   9   9 MOV(03,A,M) AA      0.700596     0.109703E-01 0.679094     0.722097    
  10  10 SRV(03,A,M) A       0.689415     0.243917E-01 0.641608     0.737223    
  11  11 MOV(03,A,M) BA      0.206115E-08 0.731985E-10 0.191768E-08 0.220462E-08
  12  12 SRV(03,A,M) B       0.689415     0.243917E-01 0.641608     0.737223    
  13  13 p(02,A,M) A         0.401277     0.869338E-02 0.384238     0.418316    
  14  14 p(02,A,M) B         0.401096     0.794117E-02 0.385531     0.416660    
  15  15 p(03,A,M) A         0.401256     0.782581E-02 0.385917     0.416594    
  16  16 p(03,A,M) B         0.401554     0.699185E-02 0.387850     0.415258    
  17  17 p(04,A,M) A         0.400724     0.121500E-01 0.376910     0.424538    
  18  18 p(04,A,M) B         0.400616     0.114315E-01 0.378210     0.423022    
  19  19 MOV(01,A,F) AA      0.614067     0.570708E-01 0.502208     0.725926    
  20  20 SRV(01,A,F) A       0.348870     0.194838E-01 0.310682     0.387058    
  21  21 MOV(01,A,F) BA      0.206115E-08 0.368173E-09 0.133953E-08 0.278277E-08
  22  22 SRV(01,A,F) B       0.348870     0.194838E-01 0.310682     0.387058    
  23  23 MOV(02,A,F) AA      0.606850     0.461969E-01 0.516304     0.697396    
  24  24 SRV(02,A,F) A       0.390379     0.145800E-01 0.361802     0.418955    
  25  25 MOV(02,A,F) BA      0.206115E-08 0.273294E-09 0.152550E-08 0.259681E-08
  26  26 SRV(02,A,F) B       0.390379     0.145800E-01 0.361802     0.418955    
  27  27 MOV(03,A,F) AA      0.597835     0.463079E-01 0.507072     0.688599    
  28  28 SRV(03,A,F) A       0.426255     0.998868E-02 0.406677     0.445833    
  29  29 MOV(03,A,F) BA      0.206115E-08 0.236557E-09 0.159750E-08 0.252481E-08
  30  30 SRV(03,A,F) B       0.426255     0.998868E-02 0.406677     0.445833    
  31  31 p(02,A,F) A         0.288786     0.234082E-01 0.242906     0.334666    
  32  32 p(02,A,F) B         0.301926     0.205089E-01 0.261729     0.342124    
  33  33 p(03,A,F) A         0.295174     0.187755E-01 0.258374     0.331974    
  34  34 p(03,A,F) B         0.303211     0.155864E-01 0.272662     0.333760    
  35  35 p(04,A,F) A         0.301634     0.172410E-01 0.267841     0.335426    
  36  36 p(04,A,F) B         0.300044     0.123364E-01 0.275865     0.324224    

     CPU time in seconds for last procedure was    8.38

Hardware Considerations

Two versions of MSSURVIV are available for PC's. A small version which will work on older PC's running DOS without Extended memory or a math coprocessor is set up to handle up to 25 cohorts, 20 classes and 50 parameters. See appendix A to determine the possible combinations of strata and sample periods for these limits.

A larger version, compiled with a "DOS extender", requires a 386/387 or 486 PC, 640Kb RAM, and at least 10Mb of free hard disk space (although MSSURVIV will run faster with more RAM). The maximum number of cohorts, classes and parameters for this version are: 64, 64, and 250, respectively.

The source code for MSSURVIV has been successfully compiled and run on a Prime minicomputer running PrimeOS, and two different unix workstations.

The program has also been compiled for Windows and OS/2. The limitations for the Windows version are the same as the DOS extender version.

Software Installation

To install MSSURVIV on a PC simply make a sub-directory to contain the programs and copy the files from the floppy disk. The disk contains the executable program file, so no compilation is necessary unless you wish to alter the dimensions. Here are the commands to install the MSSURVIV programs onto the hard disk of a PC:

c:> mkdir mssrv
c:> cd mssrv
c:> xcopy a:*.* /s

To install MSSURVIV on other computers, a FORTRAN compiler will be required. The files must first be transferred to disk on the computer, then compiled and linked into an executable program file. A "make" file is included which will create the executable program file from the source files if the target computer has the make utility (as most Unix systems do). If the target computer doesn't have a make utility, a "batch" file is included to compile all of the routines. Most likely, the make file or batch file will have to be edited to reflect the names of the compiler and linker on the target system.

Literature Cited

Brownie, C., J.E. Hines, J.D. Nichols, K.H. Pollock, and J.B. Hestbeck. 1993. Capture-recapture studies for multiple strata including non-Markovian transition probabilities. Biometrics 49:1173-1187.

Pollock, K.H., J.D. Nichols, C. Brownie, and J.E. Hines. 1990. Statistical inference for capture-recapture experiments. Wildlife Monographs 107. 97pp.

White, G.C. 1983. Numerical estimation of survival rates from band-recovery and biotelemetry data. The Journal of Wildlife Management 47:716-728. Appendix A: Maximum number of cohorts/classes/parameters for "Movement-only" and "Memory-Movement" models.

"Movement-only" models

SAMPLE                                  STRATA
PERIODS    1          2            3              4              5               6    
   3    2/ 2/ 4    4/ 4/ 12     6/ 6/ 24       8/ 8/ 40      10/10/ 60      12/ 12/ 84 
   4    3/ 3/ 6    6/ 6/ 18     9/ 9/ 36      12/12/ 60      15/15/ 90      18/ 18/126 
   5    4/ 4/ 8    8/ 8/ 24    12/12/ 48      16/16/ 80      20/20/120      24/ 24/168 
   6    5/ 5/10   10/10/ 30    15/15/ 60      20/20/100      25/25/150      30/ 30/210 
   7    6/ 6/12   12/12/ 36    18/18/ 72      24/24/120      30/30/180      36/ 36/252 
   8    7/ 7/14   14/14/ 42    21/21/ 84      28/28/140      35/35/210      42/ 42/294 
   9    8/ 8/16   16/16/ 48    24/24/ 96      32/32/160      40/40/240      48/ 48/336 
  10    9/ 9/18   18/18/ 54    27/27/108      36/36/180      45/45/270      54/ 54/378 
  11   10/10/20   20/20/ 60    30/30/120      40/40/200      50/50/300      60/ 60/420 
  12   11/11/22   22/22/ 66    33/33/132      44/44/220      55/55/330      66/ 66/462 
  13   12/12/24   24/24/ 72    36/36/144      48/48/240      60/60/360      72/ 72/504 
  14   13/13/26   26/26/ 78    39/39/156      52/52/260      65/65/390      78/ 78/546 
  15   14/14/28   28/28/ 84    42/42/168      56/56/280      70/70/420      84/ 84/588 
  16   15/15/30   30/30/ 90    45/45/180      60/60/300      75/75/450      90/ 90/630 
  17   16/16/32   32/32/ 96    48/48/192      64/64/320      80/80/480      96/ 96/672 
  18   17/17/34   34/34/102    51/51/204      68/68/340      85/85/510     102/102/714 
  19   18/18/36   36/36/108    54/54/216      72/72/360      90/90/540     108/108/756 
  20   19/19/38   38/38/114    57/57/228      76/76/380      95/95/570     114/114/798 

"Memory-Movement" models

SAMPLE                                 STRATA
PERIODS    1          2            3            4              5               6      
   3    1/ 1/ 2    4/ 2/ 10     9/ 3/ 30    16/ 4/   68    25/ 5/  130    36/  6/  222 
   4    2/ 2/ 4    8/ 4/ 20    18/ 6/ 60    32/ 8/  136    50/10/  260    72/ 12/  444 
   5    3/ 3/ 6   12/ 6/ 30    27/ 9/ 90    48/12/  204    75/15/  390   108/ 18/  666 
   6    4/ 4/ 8   16/ 8/ 40    36/12/120    64/16/  272   100/20/  520   144/ 24/  888 
   7    5/ 5/10   20/10/ 50    45/15/150    80/20/  340   125/25/  650   180/ 30/1,110 
   8    6/ 6/12   24/12/ 60    54/18/180    96/24/  408   150/30/  780   216/ 36/1,332 
   9    7/ 7/14   28/14/ 70    63/21/210   112/28/  476   175/35/  910   252/ 42/1,554 
  10    8/ 8/16   32/16/ 80    72/24/240   128/32/  544   200/40/1,040   288/ 48/1,776 
  11    9/ 9/18   36/18/ 90    81/27/270   144/36/  612   225/45/1,170   324/ 54/1,998 
  12   10/10/20   40/20/100    90/30/300   160/40/  680   250/50/1,300   360/ 60/2,220 
  13   11/11/22   44/22/110    99/33/330   176/44/  748   275/55/1,430   396/ 66/2,442 
  14   12/12/24   48/24/120   108/36/360   192/48/  816   300/60/1,560   432/ 72/2,664 
  15   13/13/26   52/26/130   117/39/390   208/52/  884   325/65/1,690   468/ 78/2,886 
  16   14/14/28   56/28/140   126/42/420   224/56/  952   350/70/1,820   504/ 84/3,108 
  17   15/15/30   60/30/150   135/45/450   240/60/1,020   375/75/1,950   540/ 90/3,330 
  18   16/16/32   64/32/160   144/48/480   256/64/1,088   400/80/2,080   576/ 96/3,552 
  19   17/17/34   68/34/170   153/51/510   272/68/1,156   425/85/2,210   612/102/3,774 
  20   18/18/36   72/36/180   162/54/540   288/72/1,224   450/90/2,340   648/108/3,996