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I'm performing some linear mixed models for a psychological experiment. I'm not a statistician so my knowledge is limited. The basic idea is that: I have an experiment in which I model my response variable as a function of within-subject factors (Emotion, Mem) and a between-subject factor (Group). I use nlme:

fit <- lme(Score ~ Group + Emotion + Mem + Group:Mem, random= ~ 1 | Subject, 
           data = dati)

Where Group is a 2 level factor (Controls, Patients). Given that I have the assumption that the variance of the response variable is different between Controls and Patients I decided to insert a weight term for the variance weights = varIdent(form = ~1 | Group):

fit_var <- lme(Score ~ Group + Emotion + Mem + Group:Mem, 
               random = ~ 1 | Subject, data = dati,
               weights = varIdent(form = ~ 1 | Group))

My question is: if I compare these two models and the fit_var model is better (in terms of AIC, BIC, LRT) it's like testing also the variance component? In other words, can I say that allowing for the heteroscedasticity in the model, the response variable explanation is improved? Thanks!

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Yes, these models are nested and therefore you can use a likelihood ratio test to compare them. This can be simply done using the anova() function, i.e.,

anova(fit, fit_var)

A significant p-value at your prespecified significance level would indicate that allowing for different variances for the error terms for the two groups improves the fit of the model.

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  • $\begingroup$ Thanks! Can I also said that this like a test on variance? I mean if I want to statistically support the fact that the variance between groups is different I can perform an F Test or a Levene Test. However, I've been taught to limit the number of separated tests preferring a single model of analysis. In this case, if considering heteroscedasticity (i.e. different variances) improve the model fit, can I say that variances are statistically different? $\endgroup$ – Filippo Gambarota Jan 9 at 9:45

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