Class: GeneralizedLinearMixedModel
Refit generalized linear mixed-effects model
glme
— Generalized linear mixed-effects modelGeneralizedLinearMixedModel
objectGeneralized linear mixed-effects model, specified as a GeneralizedLinearMixedModel
object.
For properties and methods of this object, see GeneralizedLinearMixedModel
.
ynew
— New response vectorNew response vector, specified as an n-by-1
vector of scalar values, where n is the number
of observations used to fit glme
.
For an observation i with prior weights wip and
binomial size ni (when
applicable), the response values yi contained
in ynew
can have the following values.
Distribution | Permitted Values | Notes |
---|---|---|
Binomial |
| wip and ni are integer values > 0 |
Poisson |
| wip is an integer value > 0 |
Gamma | (0,∞) | wip ≥ 0 |
InverseGaussian | (0,∞) | wip ≥ 0 |
Normal | (–∞,∞) | wip ≥ 0 |
You can access the prior weights property wip using dot notation.
glme.ObservationInfo.Weights
Data Types: single
| double
glmenew
— Generalized linear mixed-effects modelGeneralizedLinearMixedModel
objectLoad the sample data.
load mfr
This simulated data is from a manufacturing company that operates 50 factories across the world, with each factory running a batch process to create a finished product. The company wants to decrease the number of defects in each batch, so it developed a new manufacturing process. To test the effectiveness of the new process, the company selected 20 of its factories at random to participate in an experiment: Ten factories implemented the new process, while the other ten continued to run the old process. In each of the 20 factories, the company ran five batches (for a total of 100 batches) and recorded the following data:
Flag to indicate whether the batch used the new process (newprocess
)
Processing time for each batch, in hours (time
)
Temperature of the batch, in degrees Celsius (temp
)
Categorical variable indicating the supplier (A
, B
, or C
) of the chemical used in the batch (supplier
)
Number of defects in the batch (defects
)
The data also includes time_dev
and temp_dev
, which represent the absolute deviation of time and temperature, respectively, from the process standard of 3 hours at 20 degrees Celsius.
Fit a generalized linear mixed-effects model using newprocess
, time_dev
, temp_dev
, and supplier
as fixed-effects predictors. Include a random-effects term for intercept grouped by factory
, to account for quality differences that might exist due to factory-specific variations. The response variable defects
has a Poisson distribution, and the appropriate link function for this model is log. Use the Laplace fit method to estimate the coefficients. Specify the dummy variable encoding as 'effects'
, so the dummy variable coefficients sum to 0.
The number of defects can be modeled using a Poisson distribution
This corresponds to the generalized linear mixed-effects model
where
is the number of defects observed in the batch produced by factory during batch .
is the mean number of defects corresponding to factory (where ) during batch (where ).
, , and are the measurements for each variable that correspond to factory during batch . For example, indicates whether the batch produced by factory during batch used the new process.
and are dummy variables that use effects (sum-to-zero) coding to indicate whether company C
or B
, respectively, supplied the process chemicals for the batch produced by factory during batch .
is a random-effects intercept for each factory that accounts for factory-specific variation in quality.
glme = fitglme(mfr,'defects ~ 1 + newprocess + time_dev + temp_dev + supplier + (1|factory)','Distribution','Poisson','Link','log','FitMethod','Laplace','DummyVarCoding','effects');
Use random
to simulate a new response vector from the fitted model.
rng(0,'twister'); % For reproducibility ynew = random(glme);
Refit the model using the new response vector.
glme = refit(glme,ynew)
glme = Generalized linear mixed-effects model fit by ML Model information: Number of observations 100 Fixed effects coefficients 6 Random effects coefficients 20 Covariance parameters 1 Distribution Poisson Link Log FitMethod Laplace Formula: defects ~ 1 + newprocess + time_dev + temp_dev + supplier + (1 | factory) Model fit statistics: AIC BIC LogLikelihood Deviance 469.24 487.48 -227.62 455.24 Fixed effects coefficients (95% CIs): Name Estimate SE tStat DF pValue {'(Intercept)'} 1.5738 0.18674 8.4276 94 4.0158e-13 {'newprocess' } -0.21089 0.2306 -0.91455 94 0.36277 {'time_dev' } -0.13769 0.77477 -0.17772 94 0.85933 {'temp_dev' } 0.24339 0.84657 0.2875 94 0.77436 {'supplier_C' } -0.12102 0.07323 -1.6526 94 0.10175 {'supplier_B' } 0.098254 0.066943 1.4677 94 0.14551 Lower Upper 1.203 1.9445 -0.66875 0.24696 -1.676 1.4006 -1.4375 1.9243 -0.26642 0.024381 -0.034662 0.23117 Random effects covariance parameters: Group: factory (20 Levels) Name1 Name2 Type Estimate {'(Intercept)'} {'(Intercept)'} {'std'} 0.46587 Group: Error Name Estimate {'sqrt(Dispersion)'} 1
You can use refit
and random
to
conduct a simulated likelihood ratio test or parametric bootstrap.
GeneralizedLinearMixedModel
| designMatrix
| fitted
| residuals
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