Example 13 for WOMBAT

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This example illustrates multivariate analyses with repeated records per trait – this can be tricky to model if same records for different traits are taken at the same time and others are not.

New features have been implemented to assist with this:

1. WOMBAT now insists that the option RPTCOV is specified in the parameter file!
2. WOMBAT writes out a file ''RepeatedRecordsCounts'' with some basic information on how many animals have how many records.
3. There is now a mechanism – through RPTCOV TSELECT – to specify which records are measured at the same time and thus have a non-zero error covariance and which are not.
4. Trait numbers need to be assigned so that any traits with repeated records have a lower number than traits with single records.

The data are simulated records - obtained by simulating records for 4 traits recorded on 800 animals at 5 different times. A missing value indicator (999) is used to create different pattern of missing records - note that analyses in the different sub-directories analyze different columns in the data file.

• A: Demonstrates an analysis without missing records, i.e. where all traits are recorded at the same time. This implies that there are non-zero error covariances between all traits and that the ALIGNED option is appropriate.

• B : Shows the analysis when some records are missing, but in a systematic fashion: Traits 1 and 2 have records at all 5 times, but traits 3 and 4 are only recorded for times 1 and 2. As the `missing' observations only occur for the later times, the option ALIGNED is still appropriate.

• C : Similar to B, but measurements for traits 3 and 4 are taken at times 2 and 4. This means that a time of recording indicator needs to be used to model the residual covariance structure correctly. This is done specifying TSELECT together with the name of the column in the data file which contains the time variable.

• C1 : As C, but using a multivariate random regression analysis.

• D: Illustrates the scenario where we have a trait with repeated records analysed together with traits with single records and where traits with single and repeated records are measured at different times so that
  
  1. there are no error covariances between these groups of traits and
  2. that we can `use' the error covariance to model covariances between traits due to permanent environmental effects of the animal.

&nbsp &nbsp &nbsp For this example, we use records taken at times 1 to 4 for trait 1, and records taken at time 5 for traits 2 to 4. For this case a model fitting a permanent environmental effects due to the animal for trait 1 only together with the INDESCR option is appropriate. Estimates of the error covariances between trait 1 and traits 2, 3 and 4 then reflect the permanent environmental covariance, while estimates of the (co)variances among the latter represent the sum of temporary and permanent environmental covariances.

• E: Shows the case where we have a trait with repeated records analysed together with traits with single records, but where the single records are taken at the same time as one of the repeated records, so that we need to model non-zero error covariances.
  Here we consider records for trait 1 at all 5 times, and records for traits 2 to 3 taken at time 5. Again we need the TSELECT option to model this properly. In addition, we need to use the equivalent model invoked via the PEQ option in order to separate temporary and permanent nvironmental covariances between trait 1 and the other traits. Note that permanent environmental effects are fitted for all 4 traits, but that only the corresponding covariance components which can be disentangled from the environmental covariances are reported.