Package: classreg.regr
Compact generalized linear regression model class
CompactGeneralizedLinearModel
is a compact generalized linear
regression model object. It consumes less memory than a full generalized linear
regression model (GeneralizedLinearModel
) because it does not
store the data used to fit the model. The compact model does not store the input data,
so you cannot use it to perform certain tasks. However, you can use a compact
generalized linear regression model to predict responses using new input data.
Fitting operations (fitlm
, fitglm
, ...)
automatically use compact objects when you work with tall arrays. Fitting operations
with inmemory tables and arrays produce full objects. You can use the
compact
method to make them smaller.
returns a compact generalized linear regression model compactMdl
= compact(mdl
)compactMdl
from the full generalized linear regression model mdl
. For more
information, see compact
.
mdl
— Full generalized linear regression modelGeneralizedLinearModel
objectFull generalized linear regression model, specified as a
GeneralizedLinearModel
object.
CoefficientCovariance
— Covariance matrix of coefficient estimatesThis property is readonly.
Covariance matrix of coefficient estimates, specified as a pbyp matrix of numeric values. p is the number of coefficients in the fitted model.
For details, see Coefficient Standard Errors and Confidence Intervals.
Data Types: single
 double
CoefficientNames
— Coefficient namesThis property is readonly.
Coefficient names, specified as a cell array of character vectors, each containing the name of the corresponding term.
Data Types: cell
Coefficients
— Coefficient valuesThis property is readonly.
Coefficient values, specified as a table.
Coefficients
contains one row for each coefficient and these
columns:
Estimate
— Estimated
coefficient value
SE
— Standard error
of the estimate
tStat
— tstatistic for a test that the
coefficient is zero
pValue
— pvalue for the
tstatistic
Use anova
(only for a linear regression model) or
coefTest
to perform other tests on the coefficients. Use
coefCI
to find the confidence intervals of the coefficient
estimates.
To obtain any of these columns as a vector, index into the property
using dot notation. For example, obtain the estimated coefficient vector in the model
mdl
:
beta = mdl.Coefficients.Estimate
Data Types: table
Deviance
— Deviance of fitThis property is readonly.
Deviance of fit, specified as a numeric value. Deviance is useful for comparing two models when one is a special case of the other. The difference between the deviance of the two models has a chisquare distribution with degrees of freedom equal to the difference in the number of estimated parameters between the two models. For more information on deviance, see Deviance.
Data Types: single
 double
DFE
— Degrees of freedom for errorThis property is readonly.
Degrees of freedom for the error (residuals), equal to the number of observations minus the number of estimated coefficients, specified as a positive integer.
Data Types: double
Dispersion
— Scale factor of the variance of the responseThis property is readonly.
Scale factor of the variance of the response, specified as a numeric
value. Dispersion
multiplies the variance function for
the distribution.
For example, the variance function for the binomial distribution is
p(1–p)/n, where
p is the probability parameter and
n is the sample size parameter. If
Dispersion
is near 1
, the variance
of the data appears to agree with the theoretical variance of the binomial
distribution. If Dispersion
is larger than
1
, the data are “overdispersed”
relative to the binomial distribution.
Data Types: double
DispersionEstimated
— Flag to indicate use of dispersion scale factorThis property is readonly.
Flag to indicate use of dispersion scale factor, specified as a logical
value. Use DispersionEstimated
to indicate whether
fitglm
used the
Dispersion
scale factor to compute standard errors
for the coefficients in Coefficients.SE
. If
DispersionEstimated
is false
, then
fitglm
used the theoretical value of the
variance.
DispersionEstimated
can be
false
only for 'binomial'
or 'poisson'
distributions.
To set DispersionEstimated
, set the
DispersionFlag
namevalue pair in
fitglm
.
Data Types: logical
Distribution
— Generalized distribution informationThis property is readonly.
Generalized distribution information, specified as a structure with the following fields relating to the generalized distribution.
Field  Description 

Name  Name of the distribution. Options are:
'normal' ,
'binomial' ,
'poisson' ,
'gamma' , or 'inverse
gaussian' . 
DevianceFunction  Function that computes the components of the deviance as a function of the fitted parameter values and the response values. 
VarianceFunction  Function that computes the theoretical variance for the
distribution as a function of the fitted parameter values.
When DispersionEstimated is
true , Dispersion
multiplies the variance function in the computation of the
coefficient standard errors. 
Data Types: struct
Formula
— Model informationLinearFormula
objectThis property is readonly.
Model information, specified as a LinearFormula
object.
Display the formula of the fitted model mdl
using dot
notation:
mdl.Formula
Link
— Link functionThis property is readonly.
Link function, specified as a structure with the following fields.
Field  Description 

Name  Name of the link function, or '' if
you specified the link as a function handle rather than a
character vector 
LinkFunction  The function that defines f, a function handle 
DevianceFunction  Derivative of f, a function handle 
VarianceFunction  Inverse of f, a function handle 
The link is a function f that links the distribution parameter μ to the fitted linear combination Xb of the predictors:
f(μ) = Xb.
Data Types: struct
LogLikelihood
— Log likelihoodThis property is readonly.
Log likelihood of the model distribution at the response values, specified as a numeric value. The mean is fitted from the model, and other parameters are estimated as part of the model fit.
Data Types: single
 double
ModelCriterion
— Criterion for model comparisonThis property is readonly.
Criterion for model comparison, specified as a structure with these fields:
AIC
— Akaike information criterion.
AIC = –2*logL + 2*m
, where logL
is the
loglikelihood and m
is the number of estimated
parameters.
AICc
— Akaike information criterion corrected for
the sample size. AICc = AIC + (2*m*(m+1))/(n–m–1)
, where
n
is the number of observations.
BIC
— Bayesian information criterion.
BIC = –2*logL + m*log(n)
.
CAIC
— Consistent Akaike information criterion.
CAIC = –2*logL + m*(log(n)+1)
.
Information criteria are model selection tools that you can use to compare multiple models fit to the same data. These criteria are likelihoodbased measures of model fit that include a penalty for complexity (specifically, the number of parameters). Different information criteria are distinguished by the form of the penalty.
When you compare multiple models, the model with the lowest information criterion value is the bestfitting model. The bestfitting model can vary depending on the criterion used for model comparison.
To obtain any of the criterion values as a scalar, index into the property using dot
notation. For example, obtain the AIC value aic
in the model
mdl
:
aic = mdl.ModelCriterion.AIC
Data Types: struct
NumCoefficients
— Number of model coefficientsThis property is readonly.
Number of model coefficients, specified as a positive integer.
NumCoefficients
includes coefficients that are set to zero when
the model terms are rank deficient.
Data Types: double
NumEstimatedCoefficients
— Number of estimated coefficientsThis property is readonly.
Number of estimated coefficients in the model, specified as a positive integer.
NumEstimatedCoefficients
does not include coefficients that are
set to zero when the model terms are rank deficient.
NumEstimatedCoefficients
is the degrees of freedom for
regression.
Data Types: double
NumObservations
— Number of observationsThis property is readonly.
Number of observations the fitting function used in fitting, specified
as a positive integer. NumObservations
is the
number of observations supplied in the original table, dataset,
or matrix, minus any excluded rows (set with the
'Exclude'
namevalue pair
argument) or rows with missing values.
Data Types: double
NumPredictors
— Number of predictor variablesThis property is readonly.
Number of predictor variables used to fit the model, specified as a positive integer.
Data Types: double
NumVariables
— Number of variablesThis property is readonly.
Number of variables in the input data, specified as a positive integer.
NumVariables
is the number of variables in the original table or
dataset, or the total number of columns in the predictor matrix and response
vector.
NumVariables
also includes any variables that are not used to fit
the model as predictors or as the response.
Data Types: double
PredictorNames
— Names of predictors used to fit modelThis property is readonly.
Names of predictors used to fit the model, specified as a cell array of character vectors.
Data Types: cell
ResponseName
— Response variable nameThis property is readonly.
Response variable name, specified as a character vector.
Data Types: char
Rsquared
— Rsquared value for the modelThis property is readonly.
Rsquared value for the model, specified as a structure with five fields:
Ordinary
— Ordinary (unadjusted)
Rsquared
Adjusted
— Rsquared adjusted for the number of
coefficients
LLR
— Loglikelihood ratio
Deviance
— Deviance
AdjGeneralized
— Adjusted generalized
Rsquared
The Rsquared value is the proportion of total sum of squares explained by the model.
The ordinary Rsquared value relates to the SSR
and
SST
properties:
Rsquared = SSR/SST = 1  SSE/SST
.
To obtain any of these values as a scalar, index into the property using dot notation.
For example, the adjusted Rsquared value in mdl
is
r2 = mdl.Rsquared.Adjusted
Data Types: struct
SSE
— Sum of squared errorsThis property is readonly.
Sum of squared errors (residuals), specified as a numeric value.
The Pythagorean theorem implies
SST = SSE + SSR
,
where SST
is the total sum of squares,
SSE
is the sum of squared errors, and SSR
is
the regression sum of squares.
Data Types: single
 double
SSR
— Regression sum of squaresThis property is readonly.
Regression sum of squares, specified as a numeric value. The regression sum of squares is equal to the sum of squared deviations of the fitted values from their mean.
The Pythagorean theorem implies
SST = SSE +
SSR
,
where SST
is the total sum
of squares, SSE
is the sum of squared errors,
and SSR
is the regression sum of
squares.
Data Types: single
 double
SST
— Total sum of squaresThis property is readonly.
Total sum of squares, specified as a numeric value. The total sum of squares is equal
to the sum of squared deviations of the response vector y
from the
mean(y)
.
The Pythagorean theorem implies
SST = SSE + SSR
,
where SST
is the total sum of squares,
SSE
is the sum of squared errors, and SSR
is
the regression sum of squares.
Data Types: single
 double
VariableInfo
— Information about variablesThis property is readonly.
Information about variables contained in Variables
, specified as a
table with one row for each variable and the columns described in this table.
Column  Description 

Class  Variable class, specified as a cell array of character vectors, such
as 'double' and
'categorical' 
Range  Variable range, specified as a cell array of vectors

InModel  Indicator of which variables are in the fitted model, specified as a
logical vector. The value is true if the model
includes the variable. 
IsCategorical  Indicator of categorical variables, specified as a logical vector.
The value is true if the variable is
categorical. 
VariableInfo
also includes any variables that are not used to fit
the model as predictors or as the response.
Data Types: table
VariableNames
— Names of variablesThis property is readonly.
Names of variables, specified as a cell array of character vectors.
If the fit is based on a table or dataset, this property provides the names of the variables in the table or dataset.
If the fit is based on a predictor matrix and response vector,
VariableNames
contains the values specified by the
'VarNames'
namevalue pair argument of the fitting
method. The default value of 'VarNames'
is
{'x1','x2',...,'xn','y'}
.
VariableNames
also includes any variables that are not used to fit
the model as predictors or as the response.
Data Types: cell
coefCI  Confidence intervals of coefficient estimates of generalized linear model 
coefTest  Linear hypothesis test on generalized linear regression model coefficients 
devianceTest  Analysis of deviance 
disp  Display generalized linear regression model 
feval  Evaluate generalized linear regression model prediction 
plotSlice  Plot of slices through fitted generalized linear regression surface 
predict  Predict response of generalized linear regression model 
random  Simulate responses for generalized linear regression model 
Value. To learn how value classes affect copy operations, see Copying Objects (MATLAB).
Reduce the size of a full, fitted generalized linear regression model by discarding the sample data and some information related to the fitting process.
Load the data into the workspace. The simulated sample data contains 15,000 observations and 45 predictor variables.
load(fullfile(matlabroot,'examples','stats','largedata4reg.mat'))
Fit a generalized linear regression model to the data using the first 15 predictor variables.
mdl = fitglm(X(:,1:15),Y)
mdl = Generalized linear regression model: y ~ [Linear formula with 16 terms in 15 predictors] Distribution = Normal Estimated Coefficients: Estimate SE tStat pValue ___________ __________ _______ ___________ (Intercept) 3.2903 0.00010447 31497 0 x1 0.0006461 4.9991e08 12924 0 x2 0.00024739 8.6874e08 2847.7 0 x3 9.5161e05 1.1138e07 854.38 0 x4 0.00013143 1.551e07 847.35 0 x5 7.163e05 1.9793e07 361.9 0 x6 4.5064e06 2.2247e07 20.257 4.9539e90 x7 2.6258e05 2.5462e07 103.13 0 x8 6.284e05 2.5633e07 245.15 0 x9 0.00014288 2.817e07 507.19 0 x10 2.2642e05 3.0963e07 73.127 0 x11 6.0227e05 3.1639e07 190.36 0 x12 1.1665e05 3.3921e07 34.388 1.6995e249 x13 3.8595e05 3.5601e07 108.41 0 x14 0.00010021 4.0312e07 248.57 0 x15 6.5674e06 4.1692e07 15.752 1.844e55 15000 observations, 14984 error degrees of freedom Estimated Dispersion: 0.000164 Fstatistic vs. constant model: 1.18e+07, pvalue = 0
Compact the model. The compact model discards the original sample data and some information related to the fitting process, so it uses less memory than the full model.
compactMdl = compact(mdl)
compactMdl = Compact generalized linear regression model: y ~ [Linear formula with 16 terms in 15 predictors] Distribution = Normal Estimated Coefficients: Estimate SE tStat pValue ___________ __________ _______ ___________ (Intercept) 3.2903 0.00010447 31497 0 x1 0.0006461 4.9991e08 12924 0 x2 0.00024739 8.6874e08 2847.7 0 x3 9.5161e05 1.1138e07 854.38 0 x4 0.00013143 1.551e07 847.35 0 x5 7.163e05 1.9793e07 361.9 0 x6 4.5064e06 2.2247e07 20.257 4.9539e90 x7 2.6258e05 2.5462e07 103.13 0 x8 6.284e05 2.5633e07 245.15 0 x9 0.00014288 2.817e07 507.19 0 x10 2.2642e05 3.0963e07 73.127 0 x11 6.0227e05 3.1639e07 190.36 0 x12 1.1665e05 3.3921e07 34.388 1.6995e249 x13 3.8595e05 3.5601e07 108.41 0 x14 0.00010021 4.0312e07 248.57 0 x15 6.5674e06 4.1692e07 15.752 1.844e55 15000 observations, 14984 error degrees of freedom Estimated Dispersion: 0.000164 Fstatistic vs. constant model: 1.18e+07, pvalue = 0
Usage notes and limitations:
When you fit a model by using fitglm
or stepwiseglm
, the following restrictions apply.
Code generation does not support categorical predictors. You cannot
supply training data in a table that contains a logical vector,
character array, categorical array, string array, or cell array of
character vectors. Also, you cannot use the 'CategoricalVars'
namevalue pair argument. To include categorical predictors
in a model, preprocess the categorical predictors by using dummyvar
before
fitting the model.
The Link
, Derivative
, and
Inverse
fields of the 'Link'
namevalue pair argument cannot be anonymous functions. That is, you
cannot generate code using a generalized linear model that was created
using anonymous functions for links. Instead, define functions for link
components.
For more information, see Introduction to Code Generation.
GeneralizedLinearModel
 compact
 fitglm
 plotPartialDependence
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