a) Move the files BLCKDUCK.INP,  BLCKDUCK.DBF, AND BLCKDUCK.FPT from the C:\Program Files\MARK\Examples folder to your personal folders.

b) Click on the spreadsheet icon (upper left corner) and open BLCKDUCK.INP from your personal folder. The beginning of the file is shown below. You should recognize the capture history, which remember, has the form LDLDLD, where the first L indicates whether an individual was alive at the beginning of an interval, and the D indicates whether an individual died during an interval. So, 10 indicates an animal was alive at the start of an interval and survived the interval, 11 indicates an individual was alive at the start of an interval and died during the interval, and 00 indicates an individual was absent during an interval.

In the file below, there is one group and three covariates (only one of which we’re going to worry about today). Age is coded (1,0) in the first covariate column.

c) In the specifications menu we need to tell Mark that there are 8 encounter occasions, 1 group and one covariate. Name the covariate "age". Provide a title for your analysis. Then click OK.

d) One parameter index window will open (remember we don’t have to estimate encounter probability and we only have one group). We can run analyses using this PIM but our estimates will mix results from juveniles and adults (we haven’t told Mark how to handle the age covariate).

e) We need to learn one more feature of Mark, which is the Design Matrix. Click on the Design matrix button on the top toolbar and select the full Design Matrix. Design matrices specify linear models of the data in a matrix format.

For this simple case our model specifies an intercept and an adjustment for each time step (except the last one, which take on the value of the intercept). If you think about it, we require eight estimates of survival for this model and the design matrix specifies eight parameter estimates (one intercept and seven time-specific survival estimates). Run this model.

f) Before we add the age covariate to the design matrix we need to learn about the logit link. The logit is a relationship that constrains the dependent variable to take values between 0 and 1. In our case we are interested in a logit link for age. It will look like:

This will be how Mark models the relationship between age and survival. In our case age is an indicator variable taking values of 0 and 1 for subadults and adults, respectively. Thus, b ₁ provides an adjustment for the survival rate of adults relative to juveniles.

g) Now to include an age effect in our models we need to add a column to the Design Matrix for age. Right click on one of the cells in column 2 of the design matrix. A menu will pop up; select the feature for adding one column to the design matrix. A new column will appear; type age (remember we named the covariate "age") into each cell of this column down to the last row with a one for the intercept. This tells Mark we want to add an age term, that will be constant for each time step, that is we are estimating an age effect that will provide a constant difference between juveniles and adults for each time step. Run this model. Examine the real parameters and the b s. b ₁ provides an adjustment of adults relative for juveniles using the logit link. Parameter two in the table of b s provides the age adjustment. Combining the intercept and the b s for each time step will enable you to estimate survival probability for each time step for juveniles (X = 0). You can also do the calculations for adults by adding the adjustment for age. We would classify this model as an age + t model (the two ages vary in parallel across time steps).

h) If we wanted to allow the age effect to vary across time steps we would add the age effect to each of the diagonal elements in the Design matrix (after removing the age column we added earlier). This version of the Design Matrix tells Mark that we need to estimate an age effect for each time step. Go ahead an run this model and examine the real and b estimates.

a) For our purposes we are going to restrict ourselves to simple nest success models. Copy the Bart and Robson .inp, .dbf and .fpt files from the Mark Examples subdirectory to your personal directory.

b) In the Analysis specification menu we need to open this file and specify the number of encounter occasions and number of groups. The number of days nests in the sample were exposed is the number of occasions (Mark will provide an estimate of survival probability for each exposure day).

c) Run the t*g, t, g, and (.) models for these data.

d) One more class of models we haven’t considered yet are t+g models. We need the Design matrix to produce these models. The Design Matrix for thee models has a column for the model intercept, a column defining the groups and diagonals defining time-specific survival for each group. One additional diagonal adjusts the time-specific survival parameters of group 1 versus group 2. If we eliminate the additional diagonal we force the daily survival rates of the two groups to vary in parallel (there is no separate adjustment of group 1 relative to group 2 at each time step.