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Display linear mixed-effects model



display(lme) displays the fitted linear mixed-effects model lme.

Input Arguments

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Linear mixed-effects model, specified as a LinearMixedModel object constructed using fitlme or fitlmematrix.


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Load the sample data.


The dataset array shows the absolute deviations from the target quality characteristic measured from the products that five operators manufacture during three shifts, morning, evening, and night. This is a randomized block design, where the operators are the blocks. The experiment is designed to study the impact of the time of shift on the performance. The performance measure is the absolute deviation of the quality characteristics from the target value. This is simulated data.

Shift and Operator are nominal variables.

shift.Shift = nominal(shift.Shift);
shift.Operator = nominal(shift.Operator);

Fit a linear mixed-effects model with a random intercept grouped by operator to assess if performance significantly differs according to the time of the shift.

lme = fitlme(shift,'QCDev ~ Shift + (1|Operator)');

Display the model.

Linear mixed-effects model fit by ML

Model information:
    Number of observations              15
    Fixed effects coefficients           3
    Random effects coefficients          5
    Covariance parameters                2

    QCDev ~ 1 + Shift + (1 | Operator)

Model fit statistics:
    AIC       BIC       LogLikelihood    Deviance
    59.012    62.552    -24.506          49.012  

Fixed effects coefficients (95% CIs):
    Name                     Estimate    SE         tStat       DF    pValue       Lower      Upper  
    {'(Intercept)'  }         3.1196     0.88681      3.5178    12    0.0042407     1.1874     5.0518
    {'Shift_Morning'}        -0.3868     0.48344    -0.80009    12      0.43921    -1.4401    0.66653
    {'Shift_Night'  }         1.9856     0.48344      4.1072    12    0.0014535    0.93227     3.0389

Random effects covariance parameters (95% CIs):
Group: Operator (5 Levels)
    Name1                  Name2                  Type           Estimate    Lower      Upper 
    {'(Intercept)'}        {'(Intercept)'}        {'std'}        1.8297      0.94915    3.5272

Group: Error
    Name               Estimate    Lower      Upper 
    {'Res Std'}        0.76439     0.49315    1.1848

This display includes the model performance statistics, Akaike and Bayesian Information Criteria, Akaike and Bayesian Information Criteria, loglikelihood, and Deviance.

The fixed-effects coefficients table includes the names and estimates of the coefficients in the first two columns. The third column SE shows the standard errors of the coefficients. The column tStat includes the t-statistic values that correspond to each coefficient. DF is the residual degrees of freedom, and the pValue is the p-value that corresponds to the corresponding t-statistic value. The columns Lower and Upper display the lower and upper limits of a 95% confidence interval for each fixed-effects coefficient.

The first table for the random effects shows the types and the estimates of the random effects covariance parameters, with the lower and upper limits of a 95% confidence interval for each parameter. The display also shows the name of the grouping variable, operator, and the total number of levels, 5.

The second table for the random effects shows the estimate of the observation error, with the lower and upper limits of a 95% confidence interval.

More About

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[1] Hox, J. Multilevel Analysis, Techniques and Applications. Lawrence Erlbaum Associates, Inc., 2002.

[2] Stram D. O. and J. W. Lee. “Variance components testing in the longitudinal mixed-effects model”. Biometrics, Vol. 50, 4, 1994, pp. 1171–1177.