HI,

I am trying to analyse repeated measures data I have for two groups of samples using Stata 12IC. The data are defined as follows: each sample (id), group (GRP = 0/1), repeated measures timepoints (CONCEN = 0,1,2,3), dependent variable (OUT). I have previously discussed in the forum using xtmixed to create a multilevel mixed effects model ("Help with interpreting xtmixed output") with the following command:

I have belatedly realised that I presumably need to check assumptions for this model, and have been searching for assumptions of multilevel mixed effects models. I have come across several references to these, but no concise, understandable approach. And importantly, I have not been able to find what to do if your model violates one of the assumptions, e.g. if residuals are not normally distributed. This is what I have found so far:

from http://www.ats.ucla.edu/stat/stata/webbooks/reg/chapter2/statareg2.htm

- linearity: relationships between predictors and outcome variable should be linear

- Normality - the errors should be normally distributed

- Homoscedasticity: homogeneity of variance

- Independence: errors assoc with one observation are not correlated with erros of any other

- Predictor variables are measured without error

- Model specification: model should be properly specified, including all relevant variables

from https://statistics.laerd.com/statistical-guides/repeated-measures-anova-statistical-guide.php

- NORMALITY: Simliar to ANOVA, each level of the independent variable needs to be approximately normally distributed

- SPHERICITY: Similar to homogeneity of variances in between-subjects ANOVA, it is where the variances of the differences between all combinations of related groups (levels) are equal.Tested for with Mauchly's Test. Corrections can be employed in instances where the assumption of sphericity is violated: these are lower-bound estimate, Greenhouse-Geisser correction and Huynh-Feldt correction.

from Stata manual

- The overall error distribution of the linear model is assumed to be Gaussian

from http://www.griffith.edu.au/__data/assets/pdf_file/0011/439346/Stata_mixed_intro-1.pdf

- recommends adding "cov(uns)" to the options to allow unstructured covariance matrix (this is explained further with syntax in ats.ucla.edu - Repeated Measures Analysis)

My questions are:

1. What are the assumptions underlying multilevel mixed effects models?

2. Are these the same as for two way ANOVA with repeated measures?

3. What is a realistic way to check these assumptions (i.e. to ensure compliance with essential criteria)?

4. What to do if essential criteria are not met? (I say essential, as presumably there is some flexibility in adherence to criteria for most statistical tests)

Would a realistic approach be:

i. Check covariance matrix of data in wide format with

If it does not appear to be compound symmetric/exchangeable, specify an unstructured covariance as follows:

ii. predict residuals with

iii. Check normality of residuals using

Thanks

Jem

I am trying to analyse repeated measures data I have for two groups of samples using Stata 12IC. The data are defined as follows: each sample (id), group (GRP = 0/1), repeated measures timepoints (CONCEN = 0,1,2,3), dependent variable (OUT). I have previously discussed in the forum using xtmixed to create a multilevel mixed effects model ("Help with interpreting xtmixed output") with the following command:

Code:

xtmixed OUT i.GRP##c.CONCEN || id: CONCEN, mle variance

**Regression**from http://www.ats.ucla.edu/stat/stata/webbooks/reg/chapter2/statareg2.htm

- linearity: relationships between predictors and outcome variable should be linear

- Normality - the errors should be normally distributed

- Homoscedasticity: homogeneity of variance

- Independence: errors assoc with one observation are not correlated with erros of any other

- Predictor variables are measured without error

- Model specification: model should be properly specified, including all relevant variables

**Repeated measures ANOVA**from https://statistics.laerd.com/statistical-guides/repeated-measures-anova-statistical-guide.php

- NORMALITY: Simliar to ANOVA, each level of the independent variable needs to be approximately normally distributed

- SPHERICITY: Similar to homogeneity of variances in between-subjects ANOVA, it is where the variances of the differences between all combinations of related groups (levels) are equal.Tested for with Mauchly's Test. Corrections can be employed in instances where the assumption of sphericity is violated: these are lower-bound estimate, Greenhouse-Geisser correction and Huynh-Feldt correction.

**Multilevel mixed effects models**from Stata manual

- The overall error distribution of the linear model is assumed to be Gaussian

from http://www.griffith.edu.au/__data/assets/pdf_file/0011/439346/Stata_mixed_intro-1.pdf

- recommends adding "cov(uns)" to the options to allow unstructured covariance matrix (this is explained further with syntax in ats.ucla.edu - Repeated Measures Analysis)

My questions are:

1. What are the assumptions underlying multilevel mixed effects models?

2. Are these the same as for two way ANOVA with repeated measures?

3. What is a realistic way to check these assumptions (i.e. to ensure compliance with essential criteria)?

4. What to do if essential criteria are not met? (I say essential, as presumably there is some flexibility in adherence to criteria for most statistical tests)

Would a realistic approach be:

i. Check covariance matrix of data in wide format with

Code:

correlate OUT0-OUT5, cov

Code:

xtmixed OUT i.GRP##c.CONCEN || id: CONCEN, cov(uns)

Code:

predict resid, residuals

Code:

pnorm resid qnorm resid kdensity resid, normal

Jem

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