Capture-Recapture Models

CAPTURE-RECAPTURE MODELS

1) Data File and Analysis Specifications

Move the file dipper.inp from the Capture-recapture subdirectory in the class Public Folder to your personal folders.

Click the blue icon to open the Specifications Window. View the file and enter the number of encounter occasions and groups. Enter a title.

2) Analyses

a) Open the PIMs and run the S(g*t)p(g*t) model. Run the other models you can define using the PIMs [S(g) p(g*t), S(t) p(g*t), S(g*t)p(t), S(g)p(t), S(t)p(t), S(t)p(g), S(g)p(g), S(.)p(t), S(.)p(.)]. Are there other models you could run using just the PIMs?

b) We want to consider three classes of models that require the Design matrix. Retrieve the S(g*t)p(g*t) model and open the Design Matrix. Adj. To make grp 1different from grp 2 at each time step Intercept Adjustment for DESIGN MATRIIX S(g*t) group Adj. For each time step S_INT S_GRP S_T1 S_T2 S_T3 S_T4 S_T5 S_G1*T1 S_G1*T2 S_G1*T3 S_G1*T4 S_G1*T5 1 1 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 P_INT P_GRP P_T1 P_T2 P_T3 P_T4 P_T5 P_G1*T1 P_G1*T2 P_G1*T3 P_G1*T4 P_G1*T5 1 1 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0

DESIGN MATRIX

S(g+t)

S_INT S_GRP S_T1 S_T2 S_T3 S_T4 S_T5 1 1 1 0 0 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0

S_INT S_GRP 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 0 S(g+flood)

S_INT S_GRP flood 1 1 0 S_INT 1 1 S_GRP 1 TREND 1 1 1 1 1 1 1 1 1 1 0 2 1 1 1 1 0 3 1 1 1 1 0 4 1 1 0 1 0 5 1 1 0 1 1 6 1 0 1 1 0 1 1 0 0 1 1 0 0 0 2 1 1 0 0 0 3 1 0 4 1 0 5 1 0 6 S(g+TREND) Model fit and Quasi-likelihood

Remember, when goodness-of-fit testing tells us that the model doesn’t fit the data we need to be more cautious about how we interpret model selection and precision of parameter estimates. We expect the most complex model to fit the data best so we evaluate overdispersion (and other causes of lack of fit) using the most general model. (Ordinarily we would check this first before running a lot of models.). As we discussed in class, we can use the ratio of the Pearson 2/df as an assessment of overdispersion in the data. An alternative is to use the ratio deviance/df to estimate cˆ , the variance inflation factor. We then use cˆ to calculate QAICc, using the formula:

QAICc = -2log Likelihood/c-hat + 2K + 2K(K + 1)/(n-ess - K - 1), where n-ess is the effective sample size. (Note this is based on the small sample correction to AIC, AICc.) Dividing -2log Likelihood by cˆ increases the importance of the penalty term in the AICc, which will tend to favor simpler models. The overall result is that: (1) simpler models will tend to be favored; and (2) models will be more similar to each other based on their QAICc scores.

Retrieve the most general model S(g*t)p(g*t) from the Results Browser. Go to the Tests button on the menu. Select the Program Release GOF. This will run Release and report an overall 2 for Tests 2 and 3. Scroll down the output until you find these results. Calculate cˆ from the 2/df.

Another approach to estimating cˆ is to bootstrap the model results (create random data from the parameter estimates produced and estimate parameters from these random data). The random data produced from the bootstrap are not over dispersed so the deviances are a reflection of the range of random variation in estimation. If we do this 1000 times we can calculate the average deviance for analyses where the data meet the assumptions of independence (lack of over dispersion). The ratio of the deviance we got from our most general model to the average from the bootstrap provides another method for estimating cˆ . When this was done for the dipper data cˆ = 1.97.

Enter this value of cˆ using the adjustments button. Notice that AICc is changed to QAICc. what happens to the ordering of models and relative AICc values.

You should also check on the ratio of the deviance to df in the model output data because this may be the best assessment of cˆ for non capture-recapture data. Tyou will find the deviance and an estimate of cˆ by following the output, specific model output, numerical output sequence from the top toolbar. Deviance and cˆ are about half way down the numerical output.