How to interpret the Wald test on the output of a multilevel model?

[Jessica Rayse]

How to interpret the Wald test on the output of a multilevel model?

I have this output:


Mixed-effects REML regression Number of obs = 358
Group variable: escola Number of groups = 10
Obs per group:
min = 20
avg = 35,8
max = 48
Wald chi2(1) = 37,36
Log restricted-likelihood = -907,36347 Prob > chi2 = 0,0000


desempenho Coefficient Std. err. z P>z [95% conf. interval]

horas 1,894521 ,309959 6,11 0,000 1,287013 2,50203
_cons 7,116685 2,437727 2,92 0,004 2,338828 11,89454



Random-effects parameters Estimate Std. err. [95% conf. interval]

escola: Independent
var(horas) ,952236 ,4524954 ,3751975 2,416736
var(_cons) 55,62217 27,213 21,32062 145,1096

var(Residual) 7,04827 ,5416089 6,062808 8,193911

LR test vs. linear model: chi2(2) = 1416,11 Prob > chi2 = 0,0000

Help me?

[Clyde Schechter]

If by "Wald test" you mean the Wald chi2 statistic that is reported just above the log-likelihood statistic in the output, it is a test statistic, similar to what you might get with the -test- command of the hypothesis that all of the fixed-effect coefficients in the model (which in your case is just the single coefficient of horas) are zero. In your particular situation, it will agree pretty closely with the test that you can read out of the horas row of the coefficient table, or, for that matter, the log-likelihood test of the hypothesis that all of the fixed-effect coefficients are zero. In a model where there are several regressors instead of just one, it is a test statistic for the joint hypothesis that all of their coefficients are zero. Since most multi-variable models contain some variables that are included solely to adjust for other sources of outcome variation (i.e. "control" variables), this hypothesis is of no interest. So most of the time, you should just ignore this statistic. It is really only relevant if your model contains only regressors whose effects are of primary interest in your research questions and no "control variables."

Is that what you were asking about? Or did you have something else in mind? If so, please clarify because there is nothing anywhere in the output that is a "Wald test."

[Jessica Rayse]

Clyde Schechter
I had expressed myself wrongly. You were precise in your answer and I was able to understand. Thank you very much.