covarianceParameters
Class: GeneralizedLinearMixedModel
Extract covariance parameters of generalized linear mixed-effects model
Syntax
Description
[
also
returns an estimate of the dispersion parameter.psi
,dispersion
]
= covarianceParameters(glme
)
[
also
returns a cell array psi
,dispersion
,stats
]
= covarianceParameters(glme
)stats
containing the covariance
parameter estimates and related statistics.
[___] = covarianceParameters(
returns
any of the above output arguments using additional options specified
by one or more glme
,Name,Value
)Name,Value
pair arguments. For
example, you can specify the confidence level for the confidence limits
of covariance parameters.
Input Arguments
glme
— Generalized linear mixed-effects model
GeneralizedLinearMixedModel
object
Generalized linear mixed-effects model, specified as a GeneralizedLinearMixedModel
object.
For properties and methods of this object, see GeneralizedLinearMixedModel
.
Name-Value Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Alpha
— Significance level
0.05 (default) | scalar value in the range [0,1]
Significance level, specified as the comma-separated pair consisting of
'Alpha'
and a scalar value in the range [0,1]. For a value α, the
confidence level is 100 × (1 – α)%.
For example, for 99% confidence intervals, you can specify the confidence level as follows.
Example: 'Alpha',0.01
Data Types: single
| double
Output Arguments
psi
— Estimated prior covariance parameters
cell array
Estimated prior covariance parameters for the random-effects
predictors, returned as a cell array of length R,
where R is the number of grouping variables used
in the model. psi{r}
contains the covariance matrix
of random effects associated with grouping variable gr,
where r = 1, 2, ..., R, The
order of grouping variables in psi
is the same
as the order entered when fitting the model. For more information
on grouping variables, see Grouping Variables.
dispersion
— Dispersion parameter
scalar value
Dispersion parameter, returned as a scalar value.
stats
— Covariance parameter estimates and related statistics
cell array
Covariance parameter estimates and related statistics, returned
as a cell array of length (R + 1), where R is
the number of grouping variables used in the model. The first R cells
of stats
each contain a dataset array with the
following columns.
Column Name | Description |
---|---|
Group | Grouping variable name |
Name1 | Name of the first predictor variable |
Name2 | Name of the second predictor variable |
Type |
If If |
Estimate |
If If |
Lower | Lower limit of the confidence interval for the covariance parameter |
Upper | Upper limit of the confidence interval for the covariance parameter |
Cell R + 1 contains related statistics for the dispersion parameter.
It is recommended that the presence or absence of covariance parameters in
glme
be tested using the compare
method, which uses a
likelihood ratio test.
When fitting a GLME model using fitglme
and
one of the maximum likelihood fit methods ('Laplace'
or 'ApproximateLaplace'
), covarianceParameters
derives
the confidence intervals in stats
based on a
Laplace approximation to the log likelihood of the generalized linear
mixed-effects model.
When fitting a GLME model using fitglme
and
one of the pseudo likelihood fit methods ('MPL'
or 'REMPL'
), covarianceParameters
derives
the confidence intervals in stats
based on the
fitted linear mixed-effects model from the final pseudo likelihood
iteration.
Examples
Obtain Estimated Covariance Parameters
Load 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
, orC
) 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
orB
, 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');
Compute and display the estimate of the prior covariance parameter for the random-effects predictor.
[psi,dispersion,stats] = covarianceParameters(glme); psi{1}
ans = 0.0985
psi{1}
is an estimate of the prior covariance matrix of the first grouping variable. In this example, there is only one grouping variable (factory
), so psi{1}
is an estimate of .
Display the dispersion parameter.
dispersion
dispersion = 1
Display the estimated standard deviation of the random effect associated with the predictor. The first cell of stats
contains statistics for factory
, while the second cell contains statistics for the dispersion parameter.
stats{1}
ans = COVARIANCE TYPE: ISOTROPIC Group Name1 Name2 Type Estimate Lower Upper factory {'(Intercept)'} {'(Intercept)'} {'std'} 0.31381 0.19253 0.51148
The estimated standard deviation of the random effect associated with the predictor is 0.31381. The 95% confidence interval is [0.19253 , 0.51148]. Because the confidence interval does not contain 0, the random intercept is significant at the 5% significance level.
See Also
GeneralizedLinearMixedModel
| fitglme
| compare
| fixedEffects
| randomEffects
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