Program SURVIV User's Manual Version 1.2 -- March 1986
Gary C. White1
Environmental Science Group, MS-K495
Los Alamos National Laboratory
Los Alamos, NM 87545
(505)667-2914
1. Present Address: Department of Fishery and Wildlife Biology, Colorado State University, Fort
Collins, CO 80523 (303)491-6678.
Recent modifications(10/99) by
Jim Hines
Patuxent Wildlife Research Center
Laurel, Md. 20708
Program SURVIV (a stand alone program) is used to estimate survival rates from user specified
cell probability functions. The program reads the user specified algebraic expressions and
constructs a FORTRAN 77 subroutine that calculates the log-likelihood function. Numerical
optimization is then used to estimate the unknown parameters. Currently the program is available
for CDC-NOS, VAX-VMS, UNIX, PC-DOS, and MS-DOS operating systems. The NOS
version is written in single precision, while the VMS, UNIX, and DOS versions are written in
double precision.
The details of the syntax for each of the procedures in Program SURVIV are shown in Table 1.
As the reader works through the examples illustrating these procedures, he should occasionally
refer back to Table 1 to understand the information presented. Table 1 is a summary of each
procedure and does not provide the detailed explanations provided in the examples.
Data Analysis
Three general tasks are required to estimate survival rates with the above procedure. First, the
algebraic expressions must be read and the FORTRAN 77 subroutine constructed -- PROC
MODEL performs this task. Second, the likelihood function must be numerically maximized by
varying the parameter estimates for one or more sets of constraints on the parameters -- PROC
ESTIMATE performs this task. Finally comparisons of parameter estimates by hypothesis tests
must be made to identify the model appropriate for the observed data, performed by PROC
TEST.
Table 1. Summary of command syntax for each of the procedures and their modifiers in Program SURVIV. Modifiers enclosed in brackets indicate optional input. Program SURVIV allows comments enclosed between /* and */ symbols, and statements are delineated with semicolons.
_________________________________________________________________
PROC TITLE Any title information to be printed at top of each page;
PROC MODEL NPAR = # of S(I)'s in model;
INLINE [DECLARE] FORTRAN declaration;
COHORT = # of animals in cohort{FORTRAN STATEMENTS};
# observed: algebraic expression for cell probability;
.
.
.
repeated for up to maximum number of cells per cohort;
COHORT = repeated for up to maximum number of cohorts;
LABELS;
S(1) = identifying label;
.
.
.
S(NPAR) = identifying label;
PROC ESTIMATE [NSIG = # of significant digits to find for
estimates (default is 5)]
[MAXFN = maximum number of function evaluations
(default is 1000)]
[NAME = name of submodel]
[TRANSFORM = NONE or ABS (default is SIN
transform)]
[NOVAR (Do not print variance-covariance matrix,
default is to print matrix)];
INITIAL;
S(1) = value;
.
.
.
S(NPAR) = value;
or ALL = value;
or RETAIN = modname /* Obtain initial estimates from
output of previous model named in "modname" */
CONSTRAINTS /*Constraints of the form */;
S(1) = S(2) /* S(1) is the same as S(2) */ ;
S(1) < S(2) /* S(1) is less than S(2) */ ;
S(1) > S(2) /* S(1) is greater than S(2) */;
S(1) = value /* Fix parameter to constant */;
PROC TEST /* No modifiers */;
PROC BROWNIE [NSIG = # of significant digits to find for
estimates (default is 5)]
[MAXFN = maximum number of function evaluations
(default is 1000)]
[TRANSFORM = NONE or ABS (default is SIN
transform)]
[NOVAR (Do not print variance-covariance matrix,
default is to print this matrix)];
\* Input to BROWNIE is a free format version of the
input described by Brownie et al. (1978:155-158)
for programs ESTIMATE and BROWNIE, with the
additional requirement that each card image
must have a semicolon as the last non-blank
character. */;
\* Currently BROWNIE does not handle data of types
2 or 3 */;
PROC BMDPAR /* No modifiers */;
INITIAL /* As in PROC ESTIMATE */;
CONSTRAINTS /* As in PROC ESTIMATE */;
PROC IDENTIFIABLE [ADD = Constant to add for numerical derivative
(Default is 0.05)]
[MULTIPLY = Constant to multiply by for numerical derivative
(Default is 1.05)];
INITIAL /* As in PROC ESTIMATE */;
CONSTRAINTS /* As in PROC ESTIMATE */;
PROC SIMULATE [NSIM = # of replications of each simulation
(default is 5)]
[DETAIL (print details of each simulation,
with default of only simulation summaries)]
[SEED = random number seed (default is 7654321)];
[PARFILE = file name for simulated data output for
later analysis (default is no data output)]
[ERROR TEST (do not include simulations in data
summaries with warnings about convergence --
default to include questionable convergence
simulations)];
INITIAL /* As in PROC ESTIMATE */;
CONSTRAINTS /* As in PROC ESTIMATE */;
PROC SAMPLE SIZE /* Notation follows Brownie et al. 1978:190-193
*/;
S-BAR = values of S /* Define average adult survival rates.
*/;
S'-BAR = values of S' /* Define average young survival
rates. */;
F-BAR = values of f /* Define average adult recovery rate.
*/;
CV(S) = values of CV of S /* Define coefficients of
variation for values of S */;
CV(S') = values of CV of S' /* Define coefficient of
variation for values of S' */;
K = number of years /* Define number of years to
conduct banding effort. */;
PROC STOP /* Stops execution. */;
I will illustrate these procedures first with a simple example taken from Brownie et al. (1978),
page 21. Ducks were banded for 3 years, and band recoveries summarized for 5 years. The input
to run this model and the resulting output are shown in Fig. 1.
All input instructions read by Program SURVIV are echoed in the output with the identifying
INPUT --- to delineate them. Thus on page 1 of the output in Fig. 1, PROC TITLE is called with
a title for the run. Statements are separated by semicolons. Next PROC MODEL is called, with
the number of parameters to be estimated set to 7. Additional comments are specified to clarify
the input. PROC MODEL processes the observed data and the associated cell probability
statements. Thus the next line of input is COHORT = 1603 with a comment to identify this
cohort as the number of ducks banded in 1964. The COHORT card specifies the number of
animals that are subject to mortality in the mortality categories that follow it. Therefore the next
input statement specifies that 127 duck bands were returned, and the expected cell probability is
S(3). That is, the observed multinomial cell value is 127, and the expected cell value is
1603*S(3), but the number of animals at risk of mortality is known from the COHORT statement,
so only the expected cell probability is given. The colon (:) separates the observed number of
recoveries and the expected cell probability.
The next statement continues to describe the fate of the 1603 ducks banded in 1964. Forty-four
bands were recovered during the year 1965, with the expected cell probability being
S(1)*S(4).The cell probability statements must be FORTRAN 77 readable, as these algebraic
statements are used to construct the likelihood subroutine. The specification of observed
recoveries and expected cell probabilities continues for the 1964 cohort until 1968. At this time,
17 + 44 + 37 + 40 + 17 = 265 bands have been returned. Program SURVIV knows that the sum
of the observed cells should add up to the number of animals specified on the proceeding cohort
card. Because this is not the case, an additional cell is constructed with observed value equal to
1603 - 265 = 1338 ducks never seen again, and with expected cell probability equal to 1.0 minus
the sum of the previous 5 cells. The sum of all the cell probabilities must be 1.0. Thus if a duck
was never seen again (i.e., the band is not reported), then it falls into the last cell.
Program SURVIV - Survival Rate Estimation with User Specified Cell Probability Functions 12-JAN-84 19:43:42 Page
01
Version 1.1(VMS) Aug.,
1983
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INPUT --- PROC TITLE Banding Handbook Example from Page 21 of Brownie et al.(1978);
CPU time in seconds for last procedure was 0.05
INPUT --- PROC MODEL NPAR=7 /* Banding Handbook Page 21 */ ;
INPUT --- COHORT = 1603 /* BANDED 1964*/ ;
INPUT --- 127:S(3) /* BANDS RECOVERED IN 1964 */ ;
INPUT --- 44:S(1)*S(4) /* BANDS RECOVERED IN 1965 */ ;
INPUT --- 37:S(1)*S(2)*S(5) /* BANDS RECOVERED IN 1966 */ ;
INPUT --- 40:S(1)*S(2)*S(6) /* BANDS RECOVERED IN 1967 */ ;
INPUT --- 17:S(1)*S(2)*S(7) /* BANDS RECOVERED IN 1968 */ ;
INPUT --- COHORT = 1595 /* BANDED 1965*/ ;
INPUT --- 62:S(4) /* Bands recovered in 1965 */ ;
INPUT --- 76:S(2)*S(5) /* Bands recovered in 1966 */ ;
INPUT --- 44:S(2)*S(6) /* Bands recovered in 1967 */ ;
INPUT --- 28:S(2)*S(7) /* Bands recovered in 1968 */ ;
INPUT --- COHORT = 1157 /* BANDED 1966*/ ;
INPUT --- 82:S(5) /* BANDS RECOVERED IN 1966 */ ;
INPUT --- 61:S(6) /* BANDS RECOVERED IN 1967 */ ;
INPUT --- 24:S(7) /* BANDS RECOVERED IN 1968 */ ;
INPUT --- LABELS;
INPUT --- S(1)=Survival for 1964;
INPUT --- S(2)=Survival for 1965;
INPUT --- S(3)=RECOVERY FOR 1964;
INPUT --- S(4)=RECOVERY FOR 1965;
INPUT --- S(5)=RECOVERY FOR 1966;
INPUT --- S(6)=Survival for 1966 and recovery 1967;
INPUT --- S(7)=Survival for 1966-67 and recovery 1968;
CPU time in seconds for last procedure was 1.48
Fig. 1. Output from Program SURVIV for a banding analysis model from Brownie et al. (1978:21).
Program SURVIV - Survival Rate Estimation with User Specified Cell Probability Functions 12-JAN-84 19:43:42 Page
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Banding Handbook Example from page 21 of Brownie et al. (1978) Version 1.1 (VMS) Aug.,
1983
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INPUT --- PROC ESTIMATE NSIG=5 MAXFN=750 NAME=SV&RC_SAME /* COMBINATION OF SURVIVAL AND RECOVERY RATES
INPUT --- CONSTANT BY TIME*/;
INPUT --- INITIAL;
INPUT --- ALL=0.05;
INPUT --- CONSTRAINTS;
INPUT --- S(1)=S(2);
INPUT --- S(3)=S(4);
INPUT --- S(3)=S(5);
Number of parameters in model = 7
Number of parameters set equal = 3
Number of parameters fixed = 0
Number of parameters estimated = 4
Lower Upper
I Parameter S(I) Bound Bound Label
--- --------- ------ ----- ----- --------------------
1 1 0.050 0.000 1.000 Survival for 1964
2 1 0.050 0.000 1.000 Survival for 1965
3 2 0.050 0.000 1.000 RECOVERY FOR 1964
4 2 0.050 0.000 1.000 RECOVERY FOR 1965
5 2 0.050 0.000 1.000 RECOVERY FOR 1966
6 3 0.050 0.000 1.000 Survival for 1966 and recovery 1967
7 4 0.050 0.000 1.000 Survival for 1966-67 and recovery 1968
Final function value 2648.6431 (Error Return = 0)
Number of significant digits 7
Number of function evaluations 133
95% Confidence Interval
I Parameter S(I) Standard Error Lower Upper
--- --------- -------------- -------------- -------------- --------------
1 1 0.64058338 0.34957855E-01 0.57206599 0.70910078
2 1 0.64058338 0.34957855E-01 0.57206599 0.70910078
3 2 0.60617526E-01 0.32176157E-02 0.54310999E-01 0.66924053E-01
4 2 0.60617526E-01 0.32176157E-02 0.54310999E-01 0.66924053E-01
5 2 0.60617526E-01 0.32176157E-02 0.54310999E-01 0.66924053E-01
6 3 0.51111879E-01 0.47218499E-02 0.41857053E-01 0.60366704E-01
7 4 0.24322205E-01 0.30891896E-02 0.18267393E-01 0.30377016E-01
Program SURVIV - Survival Rate Estimation with User Specified Cell Probability Functions 12-JAN-84 19:43:42 Page
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Banding Handbook Example from Page 21 of Brownie et al.(1978) Version 1.1(VMS) Aug.,
1983
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Variance-Covariance matrix of estimates on diagonal and below,
Correlation matrix of estimates above diagonal.
| 1 2 3 4 5 6 7
---+---------------------------------------------------------------------------------------------------------
|
1 | 0.12220516E-02 1.0000000 -0.50834998 -0.50834998 -0.50834998 -0.47184568 -0.34320111
|
| 0.12220516E-02 0.12220516E-02-0.50834998 -0.50834998 -0.50834998 -0.47184568 -0.34320111
|
3 |-0.57179685E-04-0.57179685E-04 0.10353051E-04 1.0000000 1.0000000 0.19792254 0.14396070
|
4 |-0.57179685E-04-0.57179685E-04 0.10353051E-04 0.10353051E-04 1.0000000 0.19792254 0.14396070
|
5 |-0.57179685E-04-0.57179685E-04 0.10353051E-04 0.10353051E-04 0.10353051E-04 0.19792254 0.14396070
|
6 |-0.77885558E-04-0.77885558E-04 0.30070566E-05 0.30070566E-05 0.30070566E-05 0.22295866E-04 0.13951651
|
7 |-0.37062783E-04-0.37062783E-04 0.14309442E-05 0.14309442E-05 0.14309442E-05 0.20350840E-05 0.95430924E-05
Cohort Cell Observed Expected Chi-square Note
------ ---- -------- -------- ---------- -------------
1 1 127 97.170 9.158 0 < P < 1
1 2 44 62.245 5.348 0 < P < 1
1 3 37 39.873 0.207 0 < P < 1
1 4 40 33.621 1.210 0 < P < 1
1 5 17 15.999 0.063 0 < P < 1
1 6 1338 1354.092 0.191 0 < P < 1
2 1 62 96.685 12.443 0 < P < 1
2 2 76 61.935 3.194 0 < P < 1
2 3 44 52.223 1.295 0 < P < 1
2 4 28 24.851 0.399 0 < P < 1
2 5 1385 1359.307 0.486 0 < P < 1
3 1 82 70.134 2.007 0 < P < 1
3 2 61 59.136 0.059 0 < P < 1
3 3 24 28.141 0.609 0 < P < 1
3 4 990 999.588 0.092 0 < P < 1
------------------------------------------------------------
Total (Degrees of freedom = 8) 36.761
Pr(Larger Chi-square) = 0.0000
With pooling, Degrees of freedom = 8 Chi-square = 36.761
Pr(Larger Chi-square) = 0.0000
Log-likelihood = -52.874994
CPU time in seconds for last procedure was 1.86
Program SURVIV - Survival Rate Estimation with User Specified Cell Probability Functions 12-JAN-84 19:43:42 Page
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Banding Handbook Example from Page 21 of Brownie et al.(1978) Version 1.1(VMS) Aug.,
1983
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INPUT --- PROC ESTIMATE NSIG=5 MAXFN=750 NAME=GENERAL /*General model*/;
INPUT --- INITIAL;
INPUT --- RETAIN=SV&RC_SAME ;
Number of parameters in model = 7
Number of parameters set equal = 0
Number of parameters fixed = 0
Number of parameters estimated = 7
Lower Upper
I Parameter S(I) Bound Bound Label
--- --------- ------ ----- ----- --------------------
1 1 0.641 0.000 1.000 Survival for 1964
2 2 0.641 0.000 1.000 Survival for 1965
3 3 0.061 0.000 1.000 RECOVERY FOR 1964
4 4 0.061 0.000 1.000 RECOVERY FOR 1965
5 5 0.061 0.000 1.000 RECOVERY FOR 1966
6 6 0.051 0.000 1.000 Survival for 1966 and recovery 1967
7 7 0.024 0.000 1.000 Survival for 1966-67 and recovery 1968
Final function value 2632.5922 (Error Return = 0)
Number of significant digits 7
Number of function evaluations 190
95% Confidence Interval
I Parameter S(I) Standard Error Lower Upper
--- --------- -------------- -------------- -------------- --------------
1 1 0.65386329 0.67817609E-01 0.52094078 0.78678580
2 2 0.63432469 0.65052567E-01 0.50682166 0.76182772
3 3 0.79226450E-01 0.67459754E-02 0.66004339E-01 0.92448562E-01
4 4 0.40103773E-01 0.41474639E-02 0.31974743E-01 0.48232802E-01
5 5 0.68816791E-01 0.60804365E-02 0.56899135E-01 0.80734446E-01
6 6 0.51171460E-01 0.50073002E-02 0.41357151E-01 0.60985768E-01
7 7 0.24350557E-01 0.31908973E-02 0.18096398E-01 0.30604715E-01
Variance-Covariance matrix of estimates on diagonal and below,
Correlation matrix of estimates above diagonal.
| 1 2 3 4 5 6 7
---+---------------------------------------------------------------------------------------------------------
Program SURVIV - Survival Rate Estimation with User Specified Cell Probability Functions 12-JAN-84 19:43:42 Page
05
Banding Handbook Example from Page 21 of Brownie et al.(1978) Version 1.1(VMS) Aug.,
1983
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|
1 | 0.45992280E-02-0.38874199 -0.70637676E-01-0.38549334 0.16916143E-13 0.72043515E-13 0.86797202E-13
|
|-0.17150167E-02 0.42318365E-02-0.25947279E-13 0.11893140 -0.56544739 -0.51057168 -0.38126647
|
3 |-0.32316449E-04-0.11386782E-16 0.45508185E-04 0.53900554E-13-0.13003798E-13 0.16998136E-13 0.21718938E-13
|
4 |-0.10842813E-03 0.32088069E-04 0.15080669E-17 0.17201457E-04-0.36206355E-13-0.68325729E-13-0.84330358E-13
|
5 | 0.69755521E-17-0.22366158E-03-0.53339598E-18-0.91306601E-18 0.36971708E-04 0.30982260 0.23135825
|
6 | 0.24464762E-16-0.16631246E-03 0.57418214E-18-0.14189612E-17 0.94330357E-05 0.25073055E-04 0.20890532
|
7 | 0.18782830E-16-0.79141792E-04 0.46751567E-18-0.11160391E-17 0.44888239E-05 0.33378434E-05 0.10181826E-04
Cohort Cell Observed Expected Chi-square Note
------ ---- -------- -------- ---------- -------------
1 1 127 127.000 0.000 0 < P < 1
1 2 44 42.034 0.092 0 < P < 1
1 3 37 45.754 1.675 0 < P < 1
1 4 40 34.022 1.050 0 < P < 1
1 5 17 16.190 0.041 0 < P < 1
1 6 1338 1338.000 0.000 0 < P < 1
2 1 62 63.966 0.060 0 < P < 1
2 2 76 69.625 0.584 0 < P < 1
2 3 44 51.773 1.167 0 < P < 1
2 4 28 24.637 0.459 0 < P < 1
2 5 1385 1385.000 0.000 0 < P < 1
3 1 82 79.621 0.071 0 < P < 1
3 2 61 59.205 0.054 0 < P < 1
3 3 24 28.174 0.618 0 < P < 1
3 4 990 990.000 0.000 0 < P < 1
------------------------------------------------------------
Total (Degrees of freedom = 5) 5.872
Pr(Larger Chi-square) = 0.3189
With pooling, Degrees of freedom = 5 Chi-square = 5.872
Pr(Larger Chi-square) = 0.3189
Log-likelihood = -36.824115
CPU time in seconds for last procedure was 2.40
Program SURVIV - Survival Rate Estimation with User Specified Cell Probability Functions 12-JAN-84 19:43:42 Page
06
Banding Handbook Example from Page 21 of Brownie et al.(1978) Version 1.1(VMS) Aug.,
1983
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INPUT --- PROC ESTIMATE NSIG=5 MAXFN=750 NAME=SURVL_SAME /* 1964 SURVIVAL EQUALS 1965 SURVIVAL*/;
INPUT --- INITIAL;
INPUT --- RETAIN=GENERAL ;
INPUT --- CONSTRAINTS;
INPUT --- S(2)=S(1);
Number of parameters in model = 7
Number of parameters set equal = 1
Number of parameters fixed = 0
Number of parameters estimated = 6
Lower Upper
I Parameter S(I) Bound Bound Label
--- --------- ------ ----- ----- --------------------
1 1 0.654 0.000 1.000 Survival for 1964
2 1 0.654 0.000 1.000 Survival for 1965
3 2 0.079 0.000 1.000 RECOVERY FOR 1964
4 3 0.040 0.000 1.000 RECOVERY FOR 1965
5 4 0.069 0.000 1.000 RECOVERY FOR 1966
6 5 0.051 0.000 1.000 Survival for 1966 and recovery 1967
7 6 0.024 0.000 1.000 Survival for 1966-67 and recovery 1968
Final function value 2632.6078 (Error Return = 0)
Number of significant digits 10
Number of function evaluations 168
95% Confidence Interval
I Parameter S(I) Standard Error Lower Upper
--- --------- -------------- -------------- -------------- --------------
1 1 0.64393595 0.36818149E-01 0.57177238 0.71609952
2 1 0.64393595 0.36818149E-01 0.57177238 0.71609952
3 2 0.79277320E-01 0.67417990E-02 0.66063394E-01 0.92491246E-01
4 3 0.40325278E-01 0.39726728E-02 0.32538839E-01 0.48111717E-01
5 4 0.68453790E-01 0.57011518E-02 0.57279533E-01 0.79628048E-01
6 5 0.50901536E-01 0.47490351E-02 0.41593428E-01 0.60209645E-01
7 6 0.24222110E-01 0.30925154E-02 0.18160780E-01 0.30283441E-01
Variance-Covariance matrix of estimates on diagonal and below,
Correlation matrix of estimates above diagonal.
Program SURVIV - Survival Rate Estimation with User Specified Cell Probability Functions 12-JAN-84 19:43:42 Page
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Banding Handbook Example from Page 21 of Brownie et al.(1978) Version 1.1(VMS) Aug.,
1983
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| 1 2 3 4 5 6 7
---+---------------------------------------------------------------------------------------------------------
|
1 | 0.13555761E-02 1.0000000 -0.63570483E-01-0.25020257 -0.54624638 -0.48761740 -0.35633115
|
| 0.13555761E-02 0.13555761E-02-0.63570483E-01-0.25020257 -0.54624638 -0.48761740 -0.35633115
|
3 |-0.15779501E-04-0.15779501E-04 0.45451854E-04-0.13455097E-01 0.15415179E-01 0.13760657E-01 0.10055734E-01
|
4 |-0.36596243E-04-0.36596243E-04-0.36036734E-06 0.15782129E-04 0.11355109 0.10136358 0.74072419E-01
|
5 |-0.11466031E-03-0.11466031E-03 0.59249810E-06 0.25717972E-05 0.32503132E-04 0.23272711 0.17006759
|
6 |-0.85260233E-04-0.85260233E-04 0.44057551E-06 0.19123620E-05 0.63010794E-05 0.22553334E-04 0.15181413
|
7 |-0.40572111E-04-0.40572111E-04 0.20965317E-06 0.91002055E-06 0.29984447E-05 0.22296127E-05 0.95636516E-05
Cohort Cell Observed Expected Chi-square Note
------ ---- -------- -------- ---------- -------------
1 1 127 127.082 0.000 0 < P < 1
1 2 44 41.625 0.136 0 < P < 1
1 3 37 45.501 1.588 0 < P < 1
1 4 40 33.834 1.124 0 < P < 1
1 5 17 16.100 0.050 0 < P < 1
1 6 1338 1338.859 0.001 0 < P < 1
2 1 62 64.319 0.084 0 < P < 1
2 2 76 70.307 0.461 0 < P < 1
2 3 44 52.280 1.311 0 < P < 1
2 4 28 24.878 0.392 0 < P < 1
2 5 1385 1383.216 0.002 0 < P < 1
3 1 82 79.201 0.099 0 < P < 1
3 2 61 58.893 0.075 0 < P < 1
3 3 24 28.025 0.578 0 < P < 1
3 4 990 990.881 0.001 0 < P < 1
------------------------------------------------------------
Total (Degrees of freedom = 6) 5.901
Pr(Larger Chi-square) = 0.4343
With pooling, Degrees of freedom = 6 Chi-square = 5.901
Pr(Larger Chi-square) = 0.4343
Log-likelihood = -36.839708
CPU time in seconds for last procedure was 2.91
Program SURVIV - Survival Rate Estimation with User Specified Cell Probability Functions 12-JAN-84 19:43:42 Page
08
Banding Handbook Example from Page 21 of Brownie et al.(1978) Version 1.1(VMS) Aug.,
1983
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INPUT --- PROC ESTIMATE NSIG=5 MAXFN=750 NAME=REC_SAME /*CONSTANT RECOVERY RATES*/;
INPUT --- INITIAL;
INPUT --- RETAIN=GENERAL ;
INPUT --- CONSTRAINTS;
INPUT --- S(3)=S(4);
INPUT --- S(3)=S(5);
Number of parameters in model = 7
Number of parameters set equal = 2
Number of parameters fixed = 0
Number of parameters estimated = 5
Lower Upper
I Parameter S(I) Bound Bound Label
--- --------- ------ ----- ----- --------------------
1 1 0.654 0.000 1.000 Survival for 1964
2 2 0.634 0.000 1.000 Survival for 1965
3 3 0.079 0.000 1.000 RECOVERY FOR 1964
4 3 0.079 0.000 1.000 RECOVERY FOR 1965
5 3 0.079 0.000 1.000 RECOVERY FOR 1966
6 4 0.051 0.000 1.000 Survival for 1966 and recovery 1967
7 5 0.024 0.000 1.000 Survival for 1966-67 and recovery 1968
Final function value 2647.1385 (Error Return = 0)
Number of significant digits 7
Number of function evaluations 131
95% Confidence Interval
I Parameter S(I) Standard Error Lower Upper
--- --------- -------------- -------------- -------------- --------------
1 1 0.56107126 0.53357772E-01 0.45649002 0.66565249
2 2 0.72176072 0.63359611E-01 0.59757588 0.84594556
3 3 0.60639881E-01 0.32256549E-02 0.54317597E-01 0.66962164E-01
4 3 0.60639881E-01 0.32256549E-02 0.54317597E-01 0.66962164E-01
5 3 0.60639881E-01 0.32256549E-02 0.54317597E-01 0.66962164E-01
6 4 0.48934496E-01 0.47092640E-02 0.39704339E-01 0.58164654E-01
7 5 0.23286071E-01 0.30247206E-02 0.17357618E-01 0.29214523E-01
Variance-Covariance matrix of estimates on diagonal and below,
Correlation matrix of estimates above diagonal.
| 1 2 3 4 5 6 7
---+---------------------------------------------------------------------------------------------------------
|
1 | 0.28470518E-02-0.26501651 -0.29049126 -0.29049126 -0.29049126 -0.57322427E-01-0.42469136E-01
|
|-0.89594864E-03 0.40144403E-02-0.32749735 -0.32749735 -0.32749735 -0.49397615 -0.36597788
|
3 |-0.49997542E-04-0.66932676E-04 0.10404849E-04 1.0000000 1.0000000 0.19732926 0.14619764
|
4 |-0.49997542E-04-0.66932676E-04 0.10404849E-04 0.10404849E-04 1.0000000 0.19732926 0.14619764
|
5 |-0.49997542E-04-0.66932676E-04 0.10404849E-04 0.10404849E-04 0.10404849E-04 0.19732926 0.14619764
|
6 |-0.14403741E-04-0.14739119E-03 0.29975223E-05 0.29975223E-05 0.29975223E-05 0.22177167E-04 0.18809952
|
7 |-0.68541938E-05-0.70137875E-04 0.14264072E-05 0.14264072E-05 0.14264072E-05 0.26793286E-05 0.91489349E-05
Cohort Cell Observed Expected Chi-square Note
------ ---- -------- -------- ---------- -------------
1 1 127 97.206 9.132 0 < P < 1
1 2 44 54.539 2.037 0 < P < 1
1 3 37 39.364 0.142 0 < P < 1
1 4 40 31.766 2.134 0 < P < 1
1 5 17 15.116 0.235 0 < P < 1
1 6 1338 1365.009 0.534 0 < P < 1
2 1 62 96.721 12.464 0 < P < 1
2 2 76 69.809 0.549 0 < P < 1
2 3 44 56.334 2.700 0 < P < 1
2 4 28 26.807 0.053 0 < P < 1
2 5 1385 1345.329 1.170 0 < P < 1
3 1 82 70.160 1.998 0 < P < 1
3 2 61 56.617 0.339 0 < P < 1
3 3 24 26.942 0.321 0 < P < 1
3 4 990 1003.280 0.176 0 < P < 1
------------------------------------------------------------
Total (Degrees of freedom = 7) 33.985
Pr(Larger Chi-square) = 0.0000
With pooling, Degrees of freedom = 7 Chi-square = 33.985
Pr(Larger Chi-square) = 0.0000
Log-likelihood = -51.370480
CPU time in seconds for last procedure was 1.44
INPUT --- PROC TEST;
Submodel Name Log-likelihood NDF G-O-F
-------- ---------- -------------- --- ------
1 SV&RC_SAME -52.874994 8 0.0000
2 GENERAL -36.824115 5 0.3189
3 SURVL_SAME -36.839708 6 0.4343
4 REC_SAME -51.370480 7 0.0000
GENERAL VS. SV&RC_SAME Chi-square = 32.102 D.F. = 3 Pr(Larger Chi-square) = 0.0000
SURVL_SAME VS. SV&RC_SAME Chi-square = 32.071 D.F. = 2 Pr(Larger Chi-square) = 0.0000
REC_SAME VS. SV&RC_SAME Chi-square = 3.009 D.F. = 1 Pr(Larger Chi-square) = 0.0828
GENERAL VS. SURVL_SAME Chi-square = 0.031 D.F. = 1 Pr(Larger Chi-square) = 0.8598
GENERAL VS. REC_SAME Chi-square = 29.093 D.F. = 2 Pr(Larger Chi-square) = 0.0000
SURVL_SAME VS. REC_SAME Chi-square = 29.062 D.F. = 1 Pr(Larger Chi-square) = 0.0000
* * WARNING * * Sequence of models reinitialized to zero.
CPU time in seconds for last procedure was 0.08
INPUT --- PROC STOP /* End of this run. */ ;
CPU time in minutes for this job was 0.17
E X E C U T I O N S U C C E S S F U L
PROC MODEL continues to process COHORT statements and their associated cell probability statements for the ducks
banded in 1965 and 1966. Note that some of the parameters to be estimated occur in more than one cohort. This is
reasonable because the survival rate of a duck banded in 1964 and one banded in 1965 should both be the same in 1966,
assuming that the leg band is not changing the survival rate.
The LABELS statement is used to document the biological meaning of the parameters. Thus S(1) is shown to be the finite
survival rate for the year 1964. S(3) is the recovery rate for 1964. These parameters correspond to S1 and f1 in Brownie et
al. (1978:21). S(6) and S(7) are products of survival and recovery rates which are not identifiable. These "nuisance"
parameters must be in the model to estimate S(1) through S(5), but are not of much value biologically.
When PROC MODEL reaches the end of its input (signified by the PROC ESTIMATE statement), it constructs the
FORTRAN 77 subroutine and writes it to a disk file. Program SURVIV then exits, the FORTRAN 77 compiler is called
to compile the subroutine, the loader is called to place the binary code into the core image, and Program SURVIV is started
up again, only this time, the compile run option is not set on the execute line so that Program SURVIV assumes that the
version of the likelihood subroutine in the core image corresponds to the input to PROC MODEL. Thus PROC MODEL
does not stop execution when the PROC ESTIMATE statement is reached, but passes control to PROC ESTIMATE.
PROC ESTIMATE performs the numerical optimization of the likelihood function. Several parameters are specified on the
statement. NSIG = 5 tells PROC ESTIMATE to estimate the parameters to 5 significant digits. MAXFN = 750 says that
only 750 evaluations of the likelihood function are to be performed before an error is printed and optimization stopped.
NAME=GENERAL gives this model a name (up to 10 characters) to identify it later in the PROC TEST output. All the
parameters for PROC ESTIMATE have defaults, including NAME=SUBMODELii, where ii is the model number of this
PROC ESTIMATE execution.
The INITIAL statement tells PROC ESTIMATE to initialize the parameter values in preparation for optimization. ALL =
0.05 sets all the values to 0.05, i.e., S(1) = 0.05, S(2) = 0.25, ..., S(7) = 0.05. S(1) = 0.5 and S(2) = 0.7 resets the values of
S(1) and S(2).
Following the input to PROC ESTIMATE is the summary of the initial conditions for the upcoming optimization. The
initial value of each parameter, the lower bound, the upper bound, and the label are summarized in a table. After the table,
the results of the optimization procedure are printed. No errors are reported, the number of significant digits in the
estimates are 6, and 211 function cells were required. The next table summarizes the parameter values, standard errors and
95% confidence intervals. Then the variance-covariance and correlation matrix is printed for the parameter values.
Finally, a table of the observed versus expected cell probabilities is printed, and the contribution of each cell to the overall
chi-square goodness-of-fit statistic. If the model does not fit the data, this chi-square test will reject the null hypothesis.
The NOTE column provides another method to check that the model was correctly optimized. The message 0 < P < 1
indicates that the cell probability was in the interval [0 - 1]. Error messages are printed if the cell probability is not in the
[0 - 1] interval.
The next statement is another run of PROC ESTIMATE, this time to estimate the model parameters with equal survival in
1964 and 1965, and equal recovery rates in 1964, 1965, and 1966. These equalities are set with the CONSTRAINTS
statement. S(1) = S(2) sets survival rates for 1964 and 1965 equal. S(3) = S(4) and S(3) = S(5) sets 1964, 1965, and 1966
recovery rates equal.
These constraints are reflected in the summary of initial conditions, because only 4 parameters are to be estimated. The
column labeled PARAMETER in the summary table on page 004 of the output (Fig. 1) indicates the relationship between
S(1) and the parameter index. Thus S(1) and S(2) are both parameter 1, and S(3), S(4), and S(5) are all parameter 2.
In the summary of the estimation results, the values of S(1) and S(2) are identical, and likewise for S(3), S(4), and S(5).
Similarly, the variance-covariance matrix and the correlation matrix reflects that some of the parameters are constrained to
be equal.
Two additional runs of PROC ESTIMATE are made in the example output. In the first, the 1964 and 1965 survival rates
are not constrained, but the 1964, 1965, and 1966 recovery rates are all constrained equal. Thus a series of 4 models has
been generated. The most general model allows every identifiable survival and recovery rate to be estimated. The other
three models force various constraints on the estimates.
PROC TEST (page 010 of the output in Fig. 1) helps decide which of the four models is appropriate for the observed data.
Each model is summarized in a table giving the log-likelihood function value, the degrees of freedom of the model, and the
chi-square goodness-of-fit significance probability. In the example, only the GENERAL and SURVL_SAME models fit
the observed data. Both the models with recoveries constrained equal for 1964, 1965, and 1966 reject the goodness-of-fit
null hypothesis.
The next 6 lines provide the likelihood ratio test results of all pairs of models that do not have equal degrees of freedom.
Thus the first test suggests that the GENERAL model with 7 parameters does not fit the data much better than constraining
survival rates by year to be equal, because the significance level of the chi-square statistic is not less than 0.05.
However, tests of GENERAL versus either of the models with recovery rates constant by year strongly reject the null
hypothesis, further suggesting that constant recovery rates do not fit the observed data.
Thus the biologists would conclude from this analysis that constant recovery rates are not valid for the observed data, but
constant survival rates may be.
PROC ESTIMATE Fails
The chances that the numerical optimization procedure will not converge increase with the number of parameters, with
parameter estimates against their boundaries, and with model complexity. Generally the failure of the procedure to
converge will be obvious: the number of significant digits is less than what was requested, an error message is printed,
and/or some parameters never changed from their initial value.
Generally when PROC ESTIMATE does not converge properly, a warning about the possible lack of parameter
identifiability is printed. When this warning is received, the user should verify that each of the parameters can actually be
estimated with the model and data input to SURVIV. I have not found a suitable numerical approach to determine
parameter identifiability other than the error messages printed from PROC ESTIMATE. Occasionally, the numerical
optimization procedure in PROC ESTIMATE will converge, but the variance-covariance matrix of the parameter estimates
is not positive-definite. Lack of positive-definiteness of the variance-covariance matrix is a strong indication that the
problem lacks identifiability.
Determination of parameter identifiability with numerical methods is difficult because of the limited numerical precision of
any calculations performed. That is, a large problem (many parameters to be estimated) will appear to lack identifiability,
even though the parameters are actually identifiable. I have found no suitable method to distinguish numerical problems in
a large or poorly conditioned problem from the case where the parameters really are not identifiable. Thus the user must
carefully check the model input to SURVIV to verify that parameters are identifiable.
When PROC ESTIMATE does not produce reasonable answers, the user can try several things to correct the situation.
The first is change the initial parameter estimates to values closer to the true values, i.e., make better initial guesses. Use
the observed data to obtain these guesses rather than just setting the initial value to 0.5. Also, run PROC ESTIMATE with
a constrained model to obtain better estimates, and use the INITIAL; RETAIN=_______ feature of PROC ESTIMATE to
input the parameter estimates from this reduced model for the more complex model.
Second, PROC ESTIMATE allows an absolute value transformation that may improve convergence of the algorithm when one or more parameters are at their upper or lower boundaries. For example, if S(1) < 0.75 is specified as a constraint, and the optimization procedure wants to make S(1) > 0.75, a convergence problem may result. By specifying TRANSFORM = ABS on the PROC ESTIMATE statement, the difficulties with constrained parameters may disappear.
Finally, another procedure is available in SURVIV to generate input files for the BMDPAR program of the BMDP
statistical package (Dixon 1981). Two files are generated for input to BMDPAR: BMDFUN (NOS), BMDFUN.FOR
(VMS), or bmdfun.f (UNIX) contains the FORTRAN source code for the BMDPAR FUN subroutine; and BMDINP
(NOS), BMDINP.DAT (VMS) or bmdinp.d (UNIX) contains the input to BMDPAR. PROC BMDPAR utilizes the same
INITIAL and CONSTRAINT statements as PROC ESTIMATE and passes this information on to the BMDPAR program.
One advantage of using the BMDPAR program to perform the optimization is the greater flexibility to specify inequality
constraints. Once the BMDPAR input file has been generated, the user can modify it to provide constraints not handled by
SURVIV. Thus the user can modify the file of instructions to the BMDP-BMDPAR program to handle constraints such as
survival < (1. - recovery). Verification of results from SURVIV with BMDPAR is also encouraged to guard against the
possibility of a local maximum of the likelihood function being accepted as the global maximum.
Data Simulation and Sample Sizes
The preceding example illustrates the basic data analysis methods of Program SURVIV. Two additional procedures help design survival estimation studies.
PROC SIMULATE performs Monte Carlo simulations for the model defined in the preceding PROC MODEL statements. An example utilizing a simple biotelemetry experiment is shown in Fig. 2 and is also used in White (1983). The question to be answered in this simulation is whether 40 collars in year 1 and 50 collars in year 2 are enough effort to detect changes in survival rates of 0.1. Thus the first PROC ESTIMATE simulates 4 survival rates: 0.6, 0.7, 0.5, and 0.6. The second PROC ESTIMATE uses the same data, but constrains S(1) = S(2) and S(3) = S(4). Thus the PROC TEST procedure then tests for constant survival for years 1 and 2 and years 3 and 4.
Program SURVIV - Survival Rate Estimation with User Specified Cell Probability Functions 11-JAN-84 19:05:08 Page
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Version 1.1(VMS) Aug.,
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INPUT --- PROC TITLE Small Biotelemetry Example for Simulation in User's Manual;
CPU time in seconds for last procedure was 0.04
INPUT --- PROC MODEL NPAR=4 /* Simple Biotelemetry Example */;
INPUT --- COHORT = 40 /* Number of animals collared in year 1*/;
INPUT --- 0:(1.-S(1));
INPUT --- 0:S(1)*(1.-S(2));
INPUT --- 0:S(1)*S(2)*(1.-S(3));
INPUT --- 40:S(1)*S(2)*S(3);
INPUT --- COHORT = 50 /* Number of animals collared in year 2*/;
INPUT --- 0:(1.-S(2));
INPUT --- 0:S(2)*(1.-S(3));
INPUT --- 0:S(2)*S(3)*(1.-S(4));
INPUT --- 50:S(2)*S(3)*S(4);
INPUT --- LABELS;
INPUT --- S(1)=Survival rate in year 1;
INPUT --- S(2)=Survival rate in year 2;
INPUT --- S(3)=Survival rate in year 3;
INPUT --- S(4)=Survival rate in year 4;
CPU time in seconds for last procedure was 1.04
Fig. 2. Example of estimating survival rates from biotelemetry data when the data are simulated with PROC SIMULATE.
Program SURVIV - Survival Rate Estimation with User Specified Cell Probability Functions 11-JAN-84 19:05:08 Page
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Small Biotelemetry Example for Simulation in User's Manual Version 1.1(VMS) Aug.,
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INPUT --- PROC SIMULATE NSIM=200 SEED=4567555 PARFILE=SIMDATA ERROR TEST ;
INPUT --- INITIAL;
INPUT --- S(1)=0.6;
INPUT --- S(2)=0.7;
INPUT --- S(3)=0.5;
INPUT --- S(4)=0.6;
Number of parameters in model = 4
Number of parameters set equal = 0
Number of parameters fixed = 0
Number of parameters estimated = 4
Lower Upper
I Parameter S(I) Bound Bound Label
--- --------- ------ ----- ----- --------------------
1 1 0.600 0.000 1.000 Survival rate in year 1
2 2 0.700 0.000 1.000 Survival rate in year 2
3 3 0.500 0.000 1.000 Survival rate in year 3
4 4 0.600 0.000 1.000 Survival rate in year 4
INPUT --- PROC ESTIMATE NAME=GENERAL /* All parameters individually estimated */ ;
INPUT --- INITIAL;
INPUT --- S(1)=0.6;
INPUT --- S(2)=0.7;
INPUT --- S(3)=0.5;
INPUT --- S(4)=0.6;
Number of parameters in model = 4
Number of parameters set equal = 0
Number of parameters fixed = 0
Number of parameters estimated = 4
Lower Upper
I Parameter S(I) Bound Bound Label
--- --------- ------ ----- ----- --------------------
1 1 0.600 0.000 1.000 Survival rate in year 1
2 2 0.700 0.000 1.000 Survival rate in year 2
3 3 0.500 0.000 1.000 Survival rate in year 3
4 4 0.600 0.000 1.000 Survival rate in year 4
Program SURVIV - Survival Rate Estimation with User Specified Cell Probability Functions 11-JAN-84 19:05:08 Page
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INPUT --- PROC ESTIMATE NAME=CONSTRAIN /* Sets of 2 parameters constrained. */ ;
INPUT --- INITIAL;
INPUT --- S(1)=0.6;
INPUT --- S(2)=0.7;
INPUT --- S(3)=0.5;
INPUT --- S(4)=0.6;
INPUT --- CONSTRAINTS;
INPUT --- S(1)=S(2);
INPUT --- S(3)=S(4);
Number of parameters in model = 4
Number of parameters set equal = 2
Number of parameters fixed = 0
Number of parameters estimated = 2
Lower Upper
I Parameter S(I) Bound Bound Label
--- --------- ------ ----- ----- --------------------
1 1 0.600 0.000 1.000 Survival rate in year 1
2 1 0.600 0.000 1.000 Survival rate in year 2
3 2 0.500 0.000 1.000 Survival rate in year 3
4 2 0.500 0.000 1.000 Survival rate in year 4
Parameter estimates are written to the file SIMDATA
with the order being Replicate Number, Model Number,
and the parameters (S(I),SE(S(I)),I=1,NPAR)
The format used is '(8F10.6)', which generates (NPAR*2+2)/8+1 = 2 'CARDS' per model.
*** ERROR MESSAGE IER=130 FROM ROUTINE OPTMIZ
* * WARNING * * Rounding errors became dominant before parameters estimated to NSIG digits for Model CONSTRAIN
* * WARNING * * Check to be sure the parameters are identifiable, but the problem may just be ill-conditioned.
*** ERROR MESSAGE IER=130 FROM ROUTINE OPTMIZ
* * WARNING * * Rounding errors became dominant before parameters estimated to NSIG digits for Model CONSTRAIN
* * WARNING * * Check to be sure the parameters are identifiable, but the problem may just be ill-conditioned.
Program SURVIV - Survival Rate Estimation with User Specified Cell Probability Functions 11-JAN-84 19:05:08 Page
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Small Biotelemetry Example for Simulation in User's Manual Version 1.1(VMS) Aug.,
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S I M U L A T I O N R E S U L T S
MODEL GENERAL NSIM = 200 Converged = 200
MEAN SE 95% C. I.
I S(I)-Hat S(I)-Hat Lower Upper
----------------------------------------------------------------------------------------------------
1 0.60625000 0.54008596E-02 0.59566432 0.61683568 Survival rate in year 1
2 0.69703761 0.39232190E-02 0.68934810 0.70472712 Survival rate in year 2
3 0.50514662 0.47237913E-02 0.49588799 0.51440525 Survival rate in year 3
4 0.59308799 0.84027701E-02 0.57661856 0.60955741 Survival rate in year 4
MEAN SE 95% C. I.
I SE(S(I)-Hat) SE(S(I)-Hat) Lower Upper
----------------------------------------------------------------------------------------------------
1 0.76255140E-01 0.19810598E-03 0.75866852E-01 0.76643427E-01 Survival rate in year 1
2 0.52897333E-01 0.20781961E-03 0.52490007E-01 0.53304660E-01 Survival rate in year 2
3 0.69079840E-01 0.22577465E-03 0.68637322E-01 0.69522358E-01 Survival rate in year 3
4 0.11440702 0.80088804E-03 0.11283728 0.11597676 Survival rate in year 4
Results of Goodness of Fit Tests
<0.01 <0.05 <0.10 <0.50
----------------------------
3 16 28 99
S I M U L A T I O N R E S U L T S
MODEL CONSTRAIN NSIM = 200 Converged = 197
MEAN SE 95% C. I.
I S(I)-Hat S(I)-Hat Lower Upper
----------------------------------------------------------------------------------------------------
1 0.66448527 0.31448248E-02 0.65832141 0.67064912 Survival rate in year 1
2 0.66448527 0.31448248E-02 0.65832141 0.67064912 Survival rate in year 2
3 0.52493834 0.41833879E-02 0.51673890 0.53313778 Survival rate in year 3
4 0.52493834 0.41833879E-02 0.51673890 0.53313778 Survival rate in year 4
MEAN SE 95% C. I.
I SE(S(I)-Hat) SE(S(I)-Hat) Lower Upper
----------------------------------------------------------------------------------------------------
1 0.43532547E-01 0.12374531E-03 0.43290007E-01 0.43775088E-01 Survival rate in year 1
2 0.43532547E-01 0.12374531E-03 0.43290007E-01 0.43775088E-01 Survival rate in year 2
3 0.60142105E-01 0.20428022E-03 0.59741716E-01 0.60542494E-01 Survival rate in year 3
4 0.60142105E-01 0.20428022E-03 0.59741716E-01 0.60542494E-01 Survival rate in year 4
Program SURVIV - Survival Rate Estimation with User Specified Cell Probability Functions 11-JAN-84 19:05:08 Page
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Small Biotelemetry Example for Simulation in User's Manual Version 1.1(VMS) Aug.,
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Results of Goodness of Fit Tests
<0.01 <0.05 <0.10 <0.50
----------------------------
7 25 41 124
Likelihood Ratio Test Results
<0.01 <0.05 <0.10 <0.50 <1.00
-------------------------------------------------------------
GENERAL VS. CONSTRAIN 9 33 53 132 197
CPU time in seconds for last procedure was 167.20
INPUT --- PROC STOP /* Signal end of analysis */ ;
CPU time in minutes for this job was 2.80
E X E C U T I O N S U C C E S S F U L
The DETAIL specification on PROC SIMULATE causes a detailed printout of each of the simulations. Thus parameter
estimates and the chi-square goodness-of-fit table are both printed. If a large number of simulations are performed, the
output produced will be very large. Thus DETAIL should only be used with NSIM = 10 or less.
The PARFILE = file name specification on PROC SIMULATE is used to name an output file to receive the estimates and
associated standard errors for each of the parameters to be estimated for each of the PROC ESTIMATEs. This file might
be used as input to a statistical package to perform a more through analysis of the simulations than the summary printed by
PROC SIMULATE. The format of this file is documented in the output from PROC SIMULATE.
A random number seed to simulate data with PROC SIMULATE is provided in the SEED = value specification.
Generally, the seed should be a 5 or 7 digit odd random integer. Specifying the same seed for two PROC SIMULATEs
will generate identical data if the same model is used.
PROC SAMPLE SIZE is used to estimate the number of animals to band based on the methods described in Brownie et al. (1978:190-193). The example shown in Fig. 3 duplicates the example in Brownie et al. (1978:186-193).
Program SURVIV - Survival Rate Estimation with User Specified Cell Probability Functions 11-JAN-84 19:12:46 Page
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Version 1.1(VMS) Aug.,
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INPUT --- PROC TITLE Sample Size Estimation for Banding Study;
CPU time in seconds for last procedure was 0.04
INPUT --- PROC SAMPLE SIZE /* Sample size's for Brownie et al. (1978:192) example */;
INPUT --- S-BAR=0.6;
INPUT --- S'-BAR=0.5;
INPUT --- F-BAR=0.07;
INPUT --- CV(S)=0.04;
INPUT --- CV(S')=0.04 0.07 0.03;
INPUT --- K=2 10 1;
SAMPLE SIZE ESTIMATION FOLLOWING BROWNIE ET AL. 1976:190-193
NOTATION INTERPRETATION
-------- ------------------------------------------------------
S-BAR Mean adult survival rate per year
S'-BAR Mean young survival rate per year
F-BAR Mean adult recovery rate per year
CV(S) Coefficient of variation of mean adult survival rate
CV(S') Coefficient of variation of mean young survival rate
K Number of years to conduct banding effort
M Number of young to band each year
N Number of adults to band each year
Fig. 3. Example input to Program SURVIV for PROC SAMPLE SIZE and the output produced.
Program SURVIV - Survival Rate Estimation with User Specified Cell Probability Functions 11-JAN-84 19:12:46 Page
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Sample Size Estimation for Banding Study Version 1.1(VMS) Aug.,
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S-BAR S'-BAR F-BAR CV(S) CV(S') K N M
--------------------------------------------------------------------------------
0.60 0.50 0.07 0.04 0.04 2 22560 27269
0.60 0.50 0.07 0.04 0.04 3 5698 16597
0.60 0.50 0.07 0.04 0.04 4 2554 15982
0.60 0.50 0.07 0.04 0.04 5 1462 23514
0.60 0.50 0.07 0.04 0.04 6 959 736686
0.60 0.50 0.07 0.04 0.04 7 686 -16917
0.60 0.50 0.07 0.04 0.04 8 520 -7295
0.60 0.50 0.07 0.04 0.04 9 411 -4331
0.60 0.50 0.07 0.04 0.04 10 336 -2949
0.60 0.50 0.07 0.04 0.07 2 22560 6395
0.60 0.50 0.07 0.04 0.07 3 5698 2798
0.60 0.50 0.07 0.04 0.07 4 2554 1740
0.60 0.50 0.07 0.04 0.07 5 1462 1257
0.60 0.50 0.07 0.04 0.07 6 959 987
0.60 0.50 0.07 0.04 0.07 7 686 816
0.60 0.50 0.07 0.04 0.07 8 520 700
0.60 0.50 0.07 0.04 0.07 9 411 616
0.60 0.50 0.07 0.04 0.07 10 336 553
CPU time in seconds for last procedure was 0.28
- INPUT --- PROC STOP /* End of this run. */ ;
CPU time in minutes for this job was 0.01
E X E C U T I O N S U C C E S S F U L
The first number in each of the specification cards [S-BAR, S'-BAR, F-BAR, CV(S), CV(S'), and K], provides the value
for that parameter to be used in the sample size calculation. However, because a range of parameter values are usually
required, two additional values can be used to specify a range of values. Thus S-BAR = 0.1 0.5 0.1 tells PROC SAMPLE
SIZE to use a range of S from 0.1 to 0.5 in increments of 0.1. Note that specifying ranges for all 5 input parameters can
result in many pages of sample sizes to be output.
Additional Procedures
PROC STOP is used to exit the program and is provided to stop execution in a data file when additional models are
included in the file, but cannot be executed in this particular run because the wrong PROC MODEL has been loaded into
core. PROC STOP allows the stacking of multiple models in an input file, but only running the first one. A text editor can
be used to move models from within the input file to the top.
PROC BROWNIE will generate PROC ESTIMATE type output from input to the programs ESTIMATE and BROWNIE
described in Brownie et al. (1978:155-158). The fixed format requirements of these 2 programs has been relaxed, so that
free format input can be used. Each numerical entry should be separated from its neighbors by a space or comma. To use
SURVIV on this input, a semicolon must be put at the end of each card image, i.e., each card of input to the Brownie et al.
programs is treated as a statement in SURVIV. PROC BROWNIE generates the appropriate COHORT and cell
probability cards for input to PROC MODEL, lists these cards on the output, and then runs PROC MODEL to generate the
estimation subroutine. Once the estimation subroutine is loaded, PROC BROWNIE calls PROC ESTIMATE to generate
estimates and likelihood function values for the models appropriate to the type of input. Thus PROC BROWNIE can be
viewed as a combination of PROC MODEL and PROC ESTIMATE statements. PROC BROWNIE will generate each of
the models analyzed in the Brownie et al. programs, and if PROC TEST is used, test results between models can be
generated. The big advantage of using SURVIV to analyze these models is that additional hypothesis tests can be
performed by using PROC ESTIMATE to analyze models not specified in the Brownie et al. programs. For example, to
test if survival is constant for years 1970-75 but different than years 1976-1980, the appropriate constraint cards can be
used. The definitions of the S(I)'s must be read from a previous run of PROC BROWNIE unless the user is very familiar
with the coding scheme used.
PROC IDENTIFIABLE is somewhat useful in locating which pair of parameters are most highly correlated. The input
specifications ADD and MULTIPLY allow the user to determine how the parameter value is changed to calculate the
numerical derivatives used in this process. Generally PROC IDENTIFIABLE is a last resort at determining the
non-identifiable parameters in a model.
File Names and Execution Line
Program SURVIV utilizes five files: to read input from, to write output on, to construct the FORTRAN 77 subroutine on,
to construct the BMDPAR FUN subroutine on, and to construct the BMDPAR input on. The default file names for
VAX/VMS are SURVIN.DAT, SUPVLP.DAT, SUBROUT.FOR, BMDFUN.FOR, and BMDINP.DAT, for CDC/NOS
they are SURVIN, SURVLP, SUBROUT, BMDFUN, and BMDINP, and for UNIX they are survin, survlp, subrout.f,
bmdfun.f, and bmdinp.d, respectively. For DOS, the default input and output files are the keyboard and monitor,
respectively. The FORTRAN 77 routine is constructed on the EST.FOR file. Other output files are the same as the
VAX/VMS version of the program.
The input file can be modified on the execute line by specifying I=filename. Likewise, the output from Program SURVIV
can be placed on file XYZ by specifying L=XYZ on the execution line. The subroutine output file and the BMDPAR files
can be changed only by modifying the program. The DOS version of the program cannot read the execution line. Rather,
SURVIV asks for the user to enter the execution line parameters from the keyboard after the code is executed.
Besides the I and L parameters on the execution line, three additional parameters can be specified. COMPILE RUN (for
NOS just COMPILE) tells PROC MODEL to write the estimation subroutine to disk and stop execution, that is, the
correct model has not yet been replaced in the core image. If COMPILE RUN is not specified, execution proceeds
assuming that the correct model is in core. NOECHO causes the input lines to not be printed in the output. This option
can save some paper when the output is printed, but is not advised because of the difficulty in locating errors in the input.
LINES = # specifies the number of output lines to print per page, with the default LINES = 60.
Installation Guide for Mainframes
Program SURVIV is provided on a 9-track, ASCII, 1600 bpi, unlabeled tape with 3 files. The first file is the current
source code for VAX/VMS, the second is the current source code for CDC/NOS, and the third is the input for multiple
examples that run correctly, including all of the examples shown in this manual. The three files are 80 character record
lengths, blocked at 960 characters per block, giving 12 card images per block. To set up Program SURVIV on your
system, dump the appropriate source code and the input data file from the tape. Because Program SURVIV is written in
ANSI FORTRAN 77, few problems should be encountered in compiling the source code with an ANSI standard
FORTRAN 77 compiler. Versions of the code are also available for the UNIX and LTSS operating systems upon request.
The first step to implement Program SURVIV is to create an object deck (binary) file of the entire program with the
FORTRAN 77 compiler. This object file should be saved, because the likelihood function subroutine must be replaced
every time a PROC MODEL constructs a new subroutine.
Next a procedure file should be written to execute the program twice for each run, first to generate the model subroutine,
and then to execute the program with this subroutine replacing the default (null) model subroutine. The basic steps that
this procedure should perform are:
- Execute SURVIV with option COMPILE RUN specified,
- Execute the FORTRAN compiler with the subroutine file generated in the previous step,
- Replace the new object deck of subroutine EST in the SURVIV
object file, and
- Execute SURVIV again with the new EST subroutine.
Examples of this control language procedures for VAX/VMS and CDC/NOS are shown in Figs. 4 and 5, respectively. In
both cases, 3 parameters are passed when the procedure is executed: input file name, output file name, and a shortcut flag
to indicate that the current EST subroutine in the SURVIV object is correct for the PROC MODEL specifications in the
input file. Thus if multiple runs are made with the same model, the overhead of writing a subroutine, compiling it, and
replacing it in the SURVIV object are avoided by specifying the shortcut flag.
$ ! VAX/VMS Procedure file to execute SURVIV $ ! with input from P1, output on P2, and P3 $ ! used to shortcut compilation and linking $ ! of a new MODEL. $ ON ERROR THEN EXIT $ DATAFILE := "SURVIN.DAT" $ IF P1 .NES. "" THEN DATAFILE := 'P1' $ OUTFILE := "SUPVLP.LIS" $ IF P2 .NES. "" THEN OUTFILE := 'P2' $ ! Logical name SYS$DISK is defined as the user's path name $ RUNSURV :== $SYS$DISK:SURVIV.EXE $ IF P3 .NES. "" THEN GOTO SHORTCUT $ ! Copy SURVIV object from system $ COPY [SURVIV]SURVIV.OBJ SURVIV.OBJ $ LINK SURVIV/NOMAP $ RUNSURV I='DATAFILE' L='OUTFILE' COMPILE RUN $ FORTRAN/NOLIST SUBROUT $ LINK SUBROUT,SURVIV/EXECUTABLE $ SHORTCUT: CONTINUE $ RUNSURV I='DATAFILE' L='OUTFILE' $ EXIT
Fig. 4. Control language procedure for VAX/VMS operating system.
.PROC,SURVIV,DATAFIL=SURVIN,OUTFILE=SURVLP,SHORTCT=$NO$/$YES$. IFE,$SHORTCT$.NE.$YES$,SHORT. ATTACH,SURVOBJ=SURVIV/UN=SURVIV. REWIND(DATAFIL,SUBROBJ,OUTFILE) RETURN(OUTFILE) SURVOBJ(I=DATAFIL,L=OUTFILE,COMPILE) FTN5(I=SUBROUT,L=0,B=SUBROBJ,REW) LIBEDIT(I=0,L=0,B=SUBROBJ,P=SURVOBJ,N=SURVOB2) ENDIF(SHORT) RETURN(OUTFILE) REWIND(DATAFIL) SURVOB2(I=DATAFIL,L=OUTFILE) REVERT. SURVIV SUCCESSFUL EXIT. REVERT,ABORT. *** SURVIV ABORTED ***
Fig. 5. Cyber Control Language (CCL) procedure for CDC/NOS operating system.
Installation Guide for DOS Microcomputers
SURVIV is distributed on two 5 1/4 inch DSDD floppy diskettes. The first contains the source code with separate files for
each subroutine. The second floppy contains the object code generated with the Ryan-McFarland FORTRAN 77 compiler.
To run SURVIV, at least 512k of RAM is required, plus a hard disk. For most problems, the size of the SURVIV.EXE
file exceeds 360k, thus the hard disk requirement. A batch file (SURVIVE.BAT) is included on the second floppy disk to
execute SURVIV, including the compile run to create EST.FOR, executing the Ryan-McFarland compiler to generate
EST.OBJ, recreating SURVIV.EXE, and running SURVIV again to perform the numerical estimation phase of the
process. The batch file is interactive, telling the user what input to enter. Any DOS editor can be used to create the input
file. Example input is included in the SURVIN file on the floppy diskettes. A copy of this user's manual is also included
on the floppies as USERMAN.WP, to be printed with WordPerfect.
Setting Larger Program Dimensions
Program SURVIV has been set up with flexible array dimensions through the use of FORTRAN 77 PARAMETER statements. All the critical dimensions that would need to be changed for larger problems are in the INCLUDE file MODELC. These PARAMETERS are well documented with comment statements. Values which can be changed are MAXPAR (maximum number of parameters that can be estimated), MAXCHT (maximum number of COHORTS allowed in a model), MXCLAS (maximum number of probability cells within a cohort), MAXMOD (maximum number of models that can be generated with PROC ESTIMATE and then tested with PROC TEST), and MAXCHS (the maximum size of the character string holding the input buffer). DOS does not allow character strings larger than 255 characters, so MAXCHS is set to 255. This limitation means that statements longer than about 120 characters are not allowed. Also, cell probability expressions in PROC MODEL may not exceed 255 characters in the DOS version of SURVIV.
Literature Cited
Brownie, C., D. R. Anderson, K. P. Burnham, and D. S. Robson. 1978. Statistical inference from band recovery data--A handbook. U. S. Fish and Wildlife Service Res. Publ. No. 131, Washington, D. C. 212 pp.
Dixon, W. J.(ed.). 1981. BMDP Statistical Software 1981. Univ. of California Press, Berkeley, Calif. 726 pp.
White, G. C. 1983. Numerical estimation of survival rates from band recovery and biotelemetry data. J. Wildl. Manage. 47(3):716-728.