How to test the assumptions of proc MIXED?

[igforek]

Hello,

I run a proc MIXED on my data with a fixed factor (two infection status, InfStaStr = in, un) and some nested random factors (Stain=IsolStr=1,2,3,5 and Repeats per strain = IsolRepeatStr=A,B ...). The response is total fecundity, measured as number of eggs laid. I want to know if the infection status has an effect on total fecundity. I also want to know if the random factors are significant.The code is shown below: 

PROC Mixed DATA = WORK.SORTTempTableSorted covtest
PLOTS(ONLY)=ALL
METHOD=REML;
CLASS IsolStr IsolRepeatStr InfStaStr;
MODEL TotalFecundity= InfStaStr / HTYPE=3 E3;
RANDOM IsolStr IsolRepeatStrain(IsolStr) / TYPE=VC;

I am using SAS Enterprise Guide 7.1 (64-bit). I am attaching part of the output as a JPG file. The notes for the run do not indicate any problems (see attachment).

I need help with testing the assumptions of the analysis. I am confused in part becasue some sources define the assumptions in different ways (they seem different to me):

For example, The MIXED manual from SAS states the assumptions as follows:

-The data are normally distributed (Gaussian).
-The means (expected values) of the data are linear in terms of a certain set of parameters.
-The variances and covariances of the data are in terms of a different set of parameters, and they exhibit a structure matching one of those available in PROC MIXED.

Another document, the one entitled "Heteroscedasticity under the linear mixed model" states the assumption as follows:

- Normality of the random effects distribution;

- Independency of the response given the random effects i.e. independency of the errors;

- Normality of the error;

- Homoscedasticity of the error.

To make this matter more confusing to me, I have seen google searches from people asking for help to test for normality, homoscedasticity, and outliers (influential values) after running proc MIXED. My questions are:

What are the assumption to check after running proc MIXED?

How to test those assumptions and where to find clear examples of such tests?

I will be very obliged to anyone who can help.

Regards,

igforek