# Assumptions of Linear Mixed Model in SPSS

#### JuCel

##### New Member
Hey Everyone,
how can I check the assumptions for Linear Mixed Models in SPSS?
I found those assumptions:

There are five fundamental assumptions of linear mixed-effects models:
1.Within-group errors are independent with mean zero and variance σ2.
2.Within-group errors are independent of the random effects.
3.The random effects are normally distributed with mean zero and covariance matrix.
4.The random effects are independent in different groups.
5.The covariance matrix does not depend on the group.

(Assumptions Linear Mixed-Effect Models (Crawley, 2013) Crawley, M. J. (2013). The R book. John Wiley & Sons.)

#### katxt

##### Active Member
Independence is difficult to check. The best way is a well designed experiment with randomization of subjects, but even so you need to avoid, for example, twins as subjects (unless they are part of the design.) For the rest, most researchers will make the best design possible, do the investigation, and then check afterwards that the residuals are normal, and there is no pattern in the residual vs. the predicted values graph. Plenty of data helps guard against the effect of violation of the assumptions.

#### JuCel

##### New Member
Thanks a lot for the reply! Could you please explain what do you mean with "plenty of data" in this sentence: "Plenty of data helps guard against the effect of violation of the assumptions."

#### katxt

##### Active Member
Most designs have groups of data points recording the response for several subjects. These data points are assumed to be normal so that the anova theory works. As I understand it, it is not essential for these groups to be normal - it is the sampling distribution of the sample means of these groups that should be normal. If the group data is normal you can have small groups because then the sampling distribution of the sample means of these groups will be normal automatically. However, the central limit theorem says that for large samples, the sampling distribution of the mean approaches normal even if the group data is not normal. So if you have large enough samples the anova will work. How large depends on how non normal the groups are. Some folks say about 30 for a t test, but honestly, who knows. You can also try a transformation, then look at a probability plot of the residuals.

#### JuCel

##### New Member
--> My question here is can I check linearity for categorical variables?

I have I run my repeated mixed linear model in SPSS and I get this error message for my random effect: "The covariance parameter is redundant. the test statistic and confidence interval cannot be computed". I have no idea what I could have done wrong. Would be great if someone could help me!

here some information about my analysis:
Level 1: participants

Level 2: time
as covariancetype I chose Compound Symmetry

DV: „Score“

IVs:

FIXED EFFECTS:

1. Group (TG/CG, categorial)

2. Bayley cognition (metrical)

3. Sekt-2 sentences (metrical)

4. Sekt-2 words (metrical)

5. time (categorial)

6. four interaction terms:

- Group und time

-group und Bayley

-group und Setk-2 words

-group und Setk-2 sentences

RANDOM EFFECT:

1. subjects/participant ( "intercept included), covariance type is "variance component"