# Documentation

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# disp

Class: LinearMixedModel

Display linear mixed-effects model

## Syntax

``display(lme)``

## Description

example

````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`.

## Examples

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```load(fullfile(matlabroot,'examples','stats','shift.mat')); ```

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.

```disp(lme) ```
```Linear mixed-effects model fit by ML Model information: Number of observations 15 Fixed effects coefficients 3 Random effects coefficients 5 Covariance parameters 2 Formula: 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 '(Intercept)' 3.1196 0.88681 3.5178 12 0.0042407 'Shift_Morning' -0.3868 0.48344 -0.80009 12 0.43921 'Shift_Night' 1.9856 0.48344 4.1072 12 0.0014535 Lower Upper 1.1874 5.0518 -1.4401 0.66653 0.93227 3.0389 Random effects covariance parameters (95% CIs): Group: Operator (5 Levels) Name1 Name2 Type Estimate Lower '(Intercept)' '(Intercept)' 'std' 1.8297 0.94915 Upper 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 -statistic values that correspond to each coefficient. `DF` is the residual degrees of freedom, and the `pValue` is the -value that corresponds to the corresponding -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.

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## References

[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.