NaN confidence intervals for random effects generalized mixed effect model fitglme()

Hi,

I use the following line to fit a generalized linear mixed effect model on my data:

glme = fitglme(tbl, 'error ~ 1 + var1*var2 + (1+ var1*var2 | subject)', ...
                'Distribution','Binomial','Link','logit','FitMethod','Laplace',...
                'DummyVarCoding','effects')

Here is the results:

glme = 

Generalized linear mixed-effects model fit by ML

Model information:
    Number of observations          125388
    Fixed effects coefficients           4
    Random effects coefficients         72
    Covariance parameters               10
    Distribution                    Binomial
    Link                            Logit 
    FitMethod                       Laplace

Formula:
    error ~ 1 + va1*var2 + (1 + var1*var2 | subject)

Model fit statistics:
    AIC      BIC      LogLikelihood    Deviance
    67909    68045    -33941           67881   

Fixed effects coefficients (95% CIs):
    Name                   Estimate     SE            tStat      DF            pValue        Lower        Upper    
    {'(Intercept)'}           1.4242       0.24318     5.8564    1.2538e+05    4.7419e-09      0.94755       1.9008
    {'var1'        }         0.071231     0.0055598     12.812    1.2538e+05    1.4861e-37     0.060334     0.082128
    {'var2'      }         -0.12883      0.013019    -9.8958    1.2538e+05    4.4287e-23     -0.15435     -0.10332
    {'var1:var2'  }        0.0023277    0.00042286     5.5046    1.2538e+05    3.7072e-08    0.0014989    0.0031565

Random effects covariance parameters:
Group: subject (18 Levels)
    Name1                  Name2                  Type            Estimate 
    {'(Intercept)'}        {'(Intercept)'}        {'std' }           1.0232
    {'var1'        }        {'(Intercept)'}        {'corr'}          0.38145
    {'var2'      }        {'(Intercept)'}        {'corr'}         -0.43246
    {'var1:var2'  }        {'(Intercept)'}        {'corr'}          0.25889
    {'var1'        }        {'var1'        }        {'std' }         0.019984
    {'var2'      }        {'var1'        }        {'corr'}         -0.15137
    {'var1:var2'  }        {'var1'        }        {'corr'}          0.63492
    {'var2'      }        {'var2'      }        {'std' }         0.052801
    {'var1:var2'  }        {'var2'      }        {'corr'}          0.59288
    {'var1:var2'  }        {'var1:var2'  }        {'std' }        0.0013593

Group: Error
    Name                        Estimate
    {'sqrt(Dispersion)'}        1       
    
    
    

Then I use the following to get 95% confidence intervals for random effects:

[psi,dispersion,stats] = covarianceParameters(glme);

When I look at the confidence intervals, I have some NaN values:

stats{1}

ans = 

Covariance Type: FullCholesky

Group      Name1                  Name2                  Type            Estimate     Lower         Upper    
subject    {'(Intercept)'}        {'(Intercept)'}        {'std' }           1.0232       0.74346       1.4083
subject    {'var1'        }        {'(Intercept)'}        {'corr'}          0.38145           NaN          NaN
subject    {'var2'      }        {'(Intercept)'}        {'corr'}         -0.43246      -0.44369     -0.42108
subject    {'var1:var2'  }        {'(Intercept)'}        {'corr'}          0.25889       0.10277      0.40256
subject    {'var1'        }        {'var1'        }        {'std' }         0.019984      0.013642     0.029275
subject    {'var2'      }        {'var1'        }        {'corr'}         -0.15137           NaN          NaN
subject    {'var1:var2'  }        {'var1'        }        {'corr'}          0.63492       0.52744      0.72239
subject    {'var2'      }        {'var2'      }        {'std' }         0.052801      0.036326     0.076748
subject    {'var1:var2'  }        {'var2'      }        {'corr'}          0.59288           NaN          NaN
subject    {'var1:var2'  }        {'var1:var2'  }        {'std' }        0.0013593    0.00073738    0.0025057

Any idea on why I get NaN values for some of the 'corr' parameters?

Thank you.

Answer 1

[Paul]

I feel this happens often when a model is too complex for the number of supplied datapoints, i.e. it happens because there's not enough data to produce those estimates. I often end up not including interaction effects in the random effects for that reason.