residual diagnostics using mixed

[Felicia Hollingsworth]

Dear all,

I'm having some problems with the residual diagnostics of my multilevel model in Stata (using mixed). I've read all the previous threads on that topic here on Statalist but I'm still not sure whether I'm doing it correctly.

The main assumptions to check after running a mixed model (with my model being a random-intercept model with two levels, employees nested within firms) in my opinion are the normality of level-1 and level-2 residuals and homoscedasticity of level-1 residuals. I do have some questions regarding independence of level-1 and level-2 residuals, multicollinearity and linearity between predictors and the dependent variable as well.
I'd be more than thankful if you could tell me whether my approach would yield the results I'm looking for.

mixed ...
predict res, residuals
predict rstand, rstandard
predict rfit, fitted
predict res2, reffects

Normality

//normality of level-1 residuals
histogram rstand, normal
qnorm rstand
pnorm rstand
//normality of level-2 residuals
histogram res2, normal
qnorm res2
pnorm res2

Homoscedasticity

//homoscedastictiy of level-1 residuals
twoway(scatter rstand rfit), yline(0)

or is it supposed to be

twoway(scatter res rfit), yline(0)

And regarding homoscedasticity, what would some kind of rhombus-shaped graph imply? It's not fan-shaped (which would indicate heteroscedasticity) but the variance is still not the same at all points along the yline.

Independence of level-1 residuals and level-2 residuals
I've also read that level-1 residuals and level-2 residuals are supposed to be independent of each other. Would it be enough to check the correlation between them using the following code?:

pwcorr res res2

Multicollinearity
I'm testing for multicollinearity using

estat vif

after regress, is that even correct considering the fact that the variance inflation factor relies on the R-squared which is not really interpretable in multilevel modeling? Are there any other methods except for checking the correlations between the independent variables?

Linearity between the dependent variable and independent variables
I'm checking the linearity between the dependent variable and each of the independent variables (main predictors and control variables) using the following code:

acprplot depvar indepvar, lowess lsopts(bdwith(1))

Or do I only have to check the linearity between my main predictors and the dependent variable?


Thank you so much in advance, your input will be greatly appreciated!

Felicia

[Maxime Bercholz]

Hi Felicia,

This is a long shot, as your post is over two years old, but:

I am looking into residual diagnostics for multilevel mixed-effects linear models I am estimating, and I was wondering if you had any insights on the following based your own readings on the subject. In all of my models, the predicted level 1 and level 2 residuals appear to be positively correlated (using lowess). I thought it indicated misspecification, but I ran a few simulations (example below) and the same happens with a model known to be correctly specified.

matrix input C = (1,0\0,1)
capture program drop simixed
program define simixed, rclass
    args n1 n2
    clear
    set obs `n1'
    generate i = _n
    drawnorm x1 x2 u_i
    expand `n2'
    bysort i: generate t = _n
    generate e_it = rnormal()
    correlate u_i e_it
    return scalar rho_obs = r(rho)    
    mvtest correlations u_i e_it, equals(C)
    return scalar reject_obs = r(p_chi2) < .05    
    generate y = 2 * x1 + 3 * x2 + u_i + e_it
    mixed y x1 x2 || i:
    predict uhat, reffects
    predict ehat, residuals
    predict sehat, rstandard
    correlate uhat ehat
    return scalar rho_hat = r(rho)
    mvtest correlations uhat ehat, equals(C)
    return scalar reject_hat = r(p_chi2) < .05
    correlate uhat sehat
    return scalar rho_hat_std = r(rho)
    mvtest correlations uhat sehat, equals(C)
    return scalar reject_hat_std = r(p_chi2) < .05
end
simulate rho_obs = r(rho_obs) reject_obs = r(reject_obs) rho_hat = r(rho_hat) reject_hat = r(reject_hat) rho_hat_std = r(rho_hat_std) reject_hat_std = r(reject_hat_std), reps(1000): simixed 200 30
summarize rho_obs reject_obs rho_hat reject_hat rho_hat_std reject_hat_std, sep(2)

[Laura Vossen Engblom]

Hi there,

I have the same question as Felicia. How do I check the model assumptions after using mixed to fit a linear mixed-effects model? I had a look at help mixed postestimation and predict but could not find any examples for how to check the assumption of normality of residuals and homoscedasticity.