fitglm
Create generalized linear regression model
Syntax
Description
specifies which table variable contains the response data.mdl
= fitglm(tbl
,ResponseVarName
)
returns a generalized linear regression model with additional options specified by one or
more mdl
= fitglm(___,Name,Value
)Name,Value
pair arguments.
For example, you can specify which variables are categorical, the distribution of the response variable, and the link function to use.
Examples
Fit a Logistic Regression Model
Make a logistic binomial model of the probability of smoking as a function of age, weight, and sex, using a two-way interactions model.
Load the hospital
dataset array.
load hospital
dsa = hospital;
Specify the model using a formula that allows up to two-way interactions between the variables age, weight, and sex. Smoker is the response variable.
modelspec = 'Smoker ~ Age*Weight*Sex - Age:Weight:Sex';
Fit a logistic binomial model.
mdl = fitglm(dsa,modelspec,'Distribution','binomial')
mdl = Generalized linear regression model: logit(Smoker) ~ 1 + Sex*Age + Sex*Weight + Age*Weight Distribution = Binomial Estimated Coefficients: Estimate SE tStat pValue ___________ _________ ________ _______ (Intercept) -6.0492 19.749 -0.3063 0.75938 Sex_Male -2.2859 12.424 -0.18399 0.85402 Age 0.11691 0.50977 0.22934 0.81861 Weight 0.031109 0.15208 0.20455 0.83792 Sex_Male:Age 0.020734 0.20681 0.10025 0.92014 Sex_Male:Weight 0.01216 0.053168 0.22871 0.8191 Age:Weight -0.00071959 0.0038964 -0.18468 0.85348 100 observations, 93 error degrees of freedom Dispersion: 1 Chi^2-statistic vs. constant model: 5.07, p-value = 0.535
All of the p-values (under pValue
) are large. This means none of the coefficients are significant. The large -value for the test of the model, 0.535, indicates that this model might not differ statistically from a constant model.
GLM for Poisson Response
Create sample data with 20 predictors, and Poisson response using just three of the predictors, plus a constant.
rng('default') % for reproducibility X = randn(100,7); mu = exp(X(:,[1 3 6])*[.4;.2;.3] + 1); y = poissrnd(mu);
Fit a generalized linear model using the Poisson distribution.
mdl = fitglm(X,y,'linear','Distribution','poisson')
mdl = Generalized linear regression model: log(y) ~ 1 + x1 + x2 + x3 + x4 + x5 + x6 + x7 Distribution = Poisson Estimated Coefficients: Estimate SE tStat pValue _________ ________ ________ __________ (Intercept) 0.88723 0.070969 12.502 7.3149e-36 x1 0.44413 0.052337 8.4858 2.1416e-17 x2 0.0083388 0.056527 0.14752 0.88272 x3 0.21518 0.063416 3.3932 0.00069087 x4 -0.058386 0.065503 -0.89135 0.37274 x5 -0.060824 0.073441 -0.8282 0.40756 x6 0.34267 0.056778 6.0352 1.5878e-09 x7 0.04316 0.06146 0.70225 0.48252 100 observations, 92 error degrees of freedom Dispersion: 1 Chi^2-statistic vs. constant model: 119, p-value = 1.55e-22
The p
-values of 2.14e-17, 0.00069, and 1.58e-09 indicate that the coefficients of the variables x1
, x3
, and x6
are statistically significant.
Input Arguments
tbl
— Input data
table | dataset array
Input data including predictor and response variables, specified as a table or dataset array.
The predictor variables can be numeric, logical, categorical, character, or string. If
Distribution
is "binomial"
, the response
variable can be numeric, logical, character, or string. Otherwise, the response variable
must be numeric.
By default,
fitglm
takes the last variable as the response variable and the others as the predictor variables.To set a different column as the response variable, use the
ResponseVar
name-value pair argument.To use a subset of the columns as predictors, use the
PredictorVars
name-value pair argument.To define a model specification, set the
modelspec
argument using a formula or terms matrix. The formula or terms matrix specifies which columns to use as the predictor or response variables.
The variable names in a table do not have to be valid MATLAB® identifiers, but the names must not contain leading or trailing blanks. If the names are not valid, you cannot use a formula when you fit or adjust a model; for example:
You cannot specify
modelspec
using a formula.You cannot use a formula to specify the terms to add or remove when you use the
addTerms
function or theremoveTerms
function, respectively.You cannot use a formula to specify the lower and upper bounds of the model when you use the
step
orstepwiseglm
function with the name-value pair arguments'Lower'
and'Upper'
, respectively.
You can verify the variable names in tbl
by using the isvarname
function. If the variable names are
not valid, then you can convert them by using the matlab.lang.makeValidName
function.
ResponseVarName
— Name of variable to use as response
string scalar | character vector
Name of the variable to use as the response, specified as a string scalar or character vector.
ResponseVarName
indicates which variable in
tbl
contains the response data. When you specify
ResponseVarName
, you must also specify the
tbl
input argument.
Data Types: char
| string
X
— Predictor variables
matrix
Predictor variables, specified as an n-by-p matrix,
where n is the number of observations and p is
the number of predictor variables. Each column of X
represents
one variable, and each row represents one observation.
By default, there is a constant term in the model, unless you
explicitly remove it, so do not include a column of 1s in X
.
Data Types: single
| double
y
— Response variable
vector | matrix
Response variable, specified as a vector or matrix.
If
'Distribution'
is not'binomial'
, theny
must be an n-by-1 vector, where n is the number of observations. Each entry iny
is the response for the corresponding row ofX
ortbl
. The data type must be single or double.If
'Distribution'
is'binomial'
, theny
can be an n-by-1 vector or n-by-2 matrix with counts in column 1 andBinomialSize
in column 2.
Data Types: single
| double
| logical
| categorical
modelspec
— Model specification
'linear'
(default) | character vector or string scalar naming the model | t-by-(p + 1) terms matrix | character vector or string scalar formula in the form 'y ~
terms'
Model specification, specified as one of these values.
A character vector or string scalar naming the model.
Value Model Type 'constant'
Model contains only a constant (intercept) term. 'linear'
Model contains an intercept and linear term for each predictor. 'interactions'
Model contains an intercept, linear term for each predictor, and all products of pairs of distinct predictors (no squared terms). 'purequadratic'
Model contains an intercept term and linear and squared terms for each predictor. 'quadratic'
Model contains an intercept term, linear and squared terms for each predictor, and all products of pairs of distinct predictors. 'poly
ijk
'Model is a polynomial with all terms up to degree i
in the first predictor, degreej
in the second predictor, and so on. Specify the maximum degree for each predictor by using numerals 0 though 9. The model contains interaction terms, but the degree of each interaction term does not exceed the maximum value of the specified degrees. For example,'poly13'
has an intercept and x1, x2, x22, x23, x1*x2, and x1*x22 terms, where x1 and x2 are the first and second predictors, respectively.A t-by-(p + 1) matrix, or a Terms Matrix, specifying terms in the model, where t is the number of terms and p is the number of predictor variables, and +1 accounts for the response variable. A terms matrix is convenient when the number of predictors is large and you want to generate the terms programmatically.
A character vector or string scalar Formula in the form
'y ~ terms'
,where the
terms
are in Wilkinson Notation. The variable names in the formula must be variable names intbl
or variable names specified byVarnames
. Also, the variable names must be valid MATLAB identifiers.The software determines the order of terms in a fitted model by using the order of terms in
tbl
orX
. Therefore, the order of terms in the model can be different from the order of terms in the specified formula.
When you specify modelspec
, you cannot use the
PredictorVars
name-value argument to specify the predictor
variables.
Example: 'quadratic'
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.
Example: 'Distribution','normal','link','probit','Exclude',[23,59]
specifies
that the distribution of the response is normal, and instructs fitglm
to
use the probit link function and exclude the 23rd and 59th observations
from the fit.
BinomialSize
— Number of trials for binomial distribution
1 (default) | numeric scalar | numeric vector | character vector | string scalar
Number of trials for binomial distribution, that is the sample size, specified as the
comma-separated pair consisting of 'BinomialSize'
and the
variable name in tbl
, a numeric scalar, or a numeric
vector of the same length as the response. This is the parameter
n
for the fitted binomial distribution.
BinomialSize
applies only when the
Distribution
parameter is
'binomial'
.
If BinomialSize
is a scalar value, that means
all observations have the same number of trials.
As an alternative to BinomialSize
, you can specify the response as a
two-column matrix with counts in column 1 and BinomialSize
in column
2.
Data Types: single
| double
| char
| string
B0
— Initial values for coefficient estimates
numeric vector
Initial values for the coefficient estimates, specified as a numeric vector. The default values are initial fitted values derived from the input data.
Data Types: single
| double
CategoricalVars
— Categorical predictor list
string array | cell array of character vectors | logical or numeric index vector
Categorical predictor list, specified as the comma-separated pair consisting of
'CategoricalVars'
and either a string array or cell array of
character vectors containing categorical predictor names in the table or dataset array
tbl
, or a logical or numeric index vector indicating which
predictor columns are categorical.
If data is in a table or dataset array
tbl
, then, by default,fitglm
treats all categorical values, logical values, character arrays, string arrays, and cell arrays of character vectors as categorical predictors.If data is in matrix
X
, then the default value of'CategoricalVars'
is an empty matrix[]
. That is, no predictor is categorical unless you specify it as categorical.
For example, you can specify the second and third variables out of six as categorical using either of the following:
Example: 'CategoricalVars',[2,3]
Example: 'CategoricalVars',logical([0 1 1 0 0 0])
Data Types: single
| double
| logical
| string
| cell
DispersionFlag
— Indicator to compute dispersion parameter
false
for 'binomial'
and 'poisson'
distributions (default) | true
Indicator to compute dispersion parameter for 'binomial'
and 'poisson'
distributions,
specified as the comma-separated pair consisting of 'DispersionFlag'
and
one of the following.
true | Estimate a dispersion parameter when computing standard errors. The estimated dispersion parameter value is the sum of squared Pearson residuals divided by the degrees of freedom for error (DFE). |
false | Default. Use the theoretical value of 1 when computing standard errors. |
The fitting function always estimates the dispersion for other distributions.
Example: 'DispersionFlag',true
Distribution
— Distribution of the response variable
'normal'
(default) | 'binomial'
| 'poisson'
| 'gamma'
| 'inverse gaussian'
Distribution of the response variable, specified as the comma-separated
pair consisting of 'Distribution'
and one of the
following.
'normal' | Normal distribution |
'binomial' | Binomial distribution |
'poisson' | Poisson distribution |
'gamma' | Gamma distribution |
'inverse gaussian' | Inverse Gaussian distribution |
Example: 'Distribution','gamma'
Exclude
— Observations to exclude
logical or numeric index vector
Observations to exclude from the fit, specified as the comma-separated
pair consisting of 'Exclude'
and a logical or numeric
index vector indicating which observations to exclude from the fit.
For example, you can exclude observations 2 and 3 out of 6 using either of the following examples.
Example: 'Exclude',[2,3]
Example: 'Exclude',logical([0 1 1 0 0 0])
Data Types: single
| double
| logical
Intercept
— Indicator for constant term
true
(default) | false
Indicator for the constant term (intercept) in the fit, specified as the comma-separated pair
consisting of 'Intercept'
and either true
to
include or false
to remove the constant term from the model.
Use 'Intercept'
only when specifying the model using a character vector or
string scalar, not a formula or matrix.
Example: 'Intercept',false
LikelihoodPenalty
— Penalty for likelihood estimate
"none"
(default) | "jeffreys-prior"
Penalty for the likelihood estimate, specified as "none"
or
"jeffreys-prior"
.
"none"
—fitglm
does not apply a penalty to the likelihood estimate."jeffreys-prior"
—fitglm
uses Jeffreys prior to penalize the likelihood estimate.
For logistic models, setting LikelihoodPenalty
to
"jeffreys-prior"
is called Firth's
regression. To reduce the coefficient estimate bias when you have a small
number of samples, or when you are performing binomial (logistic) regression on a
separable data set, set LikelihoodPenalty
to
"jeffreys-prior"
.
Example: LikelihoodPenalty="jeffreys-prior"
Data Types: char
| string
Link
— Link function
canonical link function (default) | scalar value | structure
Link function to use in place of the canonical link function,
specified as the comma-separated pair consisting of 'Link'
and
one of the following.
Link Function Name | Link Function | Mean (Inverse) Function |
---|---|---|
'identity' | f(μ) = μ | μ = Xb |
'log' | f(μ) = log(μ) | μ = exp(Xb) |
'logit' | f(μ) = log(μ/(1–μ)) | μ = exp(Xb) / (1 + exp(Xb)) |
'probit' | f(μ) = Φ–1(μ), where Φ is the cumulative distribution function of the standard normal distribution. | μ = Φ(Xb) |
'comploglog' | f(μ) = log(–log(1 – μ)) | μ = 1 – exp(–exp(Xb)) |
'reciprocal' | f(μ) = 1/μ | μ = 1/(Xb) |
p (a number) | f(μ) = μp | μ = Xb1/p |
| f(μ) = S.Link (μ) | μ = S.Inverse (Xb) |
The link function defines the relationship f(μ) = X*b between the mean response μ and the linear combination of predictors X*b.
For more information on the canonical link functions, see Canonical Link Function.
Example: 'Link','probit'
Data Types: char
| string
| single
| double
| struct
Options
— Optimization options
statset('fitglm
')
(default) | structure
fitglm
')Optimization options, specified as a structure. This argument determines the control
parameters for the iterative algorithm that fitglm
uses.
Create the 'Options'
value by using the function statset
or by creating a structure array containing the fields and values described in this table.
Field Name | Value | Default Value |
---|---|---|
Display | Amount of information displayed by the algorithm
| 'off' |
MaxIter | Maximum number of iterations allowed, specified as a positive integer | 100 |
TolX | Termination tolerance for the parameters, specified as a positive scalar | 1e-6 |
You can also enter statset('
in the
Command Window to see the names and default values of the fields that
fitglm
')fitglm
accepts in the 'Options'
name-value argument.
Example: 'Options',statset('Display','final','MaxIter',1000)
specifies to display the final information of the iterative algorithm results, and change the maximum number of iterations allowed to 1000.
Data Types: struct
Offset
— Offset variable
[ ] (default) | numeric vector | character vector | string scalar
Offset variable in the fit, specified as the comma-separated pair consisting of
'Offset'
and the variable name in
tbl
or a numeric vector with the same length as
the response.
fitglm
uses Offset
as an additional predictor
with a coefficient value fixed at 1. In other words, the formula for fitting is
f(μ) =
Offset +
X*b
,
where f is the link function,
μ is the mean response, and
X*b is the linear combination
of predictors X. The Offset
predictor
has coefficient 1
.
For example, consider a Poisson regression model. Suppose the
number of counts is known for theoretical reasons to be proportional
to a predictor A
. By using the log link function
and by specifying log(A)
as an offset, you can
force the model to satisfy this theoretical constraint.
Data Types: single
| double
| char
| string
PredictorVars
— Predictor variables
string array | cell array of character vectors | logical or numeric index vector
Predictor variables to use in the fit, specified as the comma-separated pair consisting of
'PredictorVars'
and either a string array or cell array of
character vectors of the variable names in the table or dataset array
tbl
, or a logical or numeric index vector indicating which
columns are predictor variables.
The string values or character vectors should be among the names in tbl
, or
the names you specify using the 'VarNames'
name-value pair
argument.
The default is all variables in X
, or all
variables in tbl
except for ResponseVar
.
For example, you can specify the second and third variables as the predictor variables using either of the following examples.
When you specify PredictorVars
, you cannot use the
modelspec
input argument to specify a terms matrix.
Example: 'PredictorVars',[2,3]
Example: 'PredictorVars',logical([0 1 1 0 0 0])
Data Types: single
| double
| logical
| string
| cell
ResponseVar
— Response variable
last column in tbl
(default) | character vector or string scalar containing variable name | logical or numeric index vector
Response variable to use in the fit, specified as the comma-separated pair consisting of
'ResponseVar'
and either a character vector or string scalar
containing the variable name in the table or dataset array tbl
, or a
logical or numeric index vector indicating which column is the response variable. You
typically need to use 'ResponseVar'
when fitting a table or dataset
array tbl
.
For example, you can specify the fourth variable, say yield
,
as the response out of six variables, in one of the following ways.
Example: 'ResponseVar','yield'
Example: 'ResponseVar',[4]
Example: 'ResponseVar',logical([0 0 0 1 0 0])
Data Types: single
| double
| logical
| char
| string
VarNames
— Names of variables
{'x1','x2',...,'xn','y'}
(default) | string array | cell array of character vectors
Names of variables, specified as the comma-separated pair consisting of
'VarNames'
and a string array or cell array of character vectors
including the names for the columns of X
first, and the name for the
response variable y
last.
'VarNames'
is not applicable to variables in a table or dataset
array, because those variables already have names.
The variable names do not have to be valid MATLAB identifiers, but the names must not contain leading or trailing blanks. If the names are not valid, you cannot use a formula when you fit or adjust a model; for example:
You cannot use a formula to specify the terms to add or remove when you use the
addTerms
function or theremoveTerms
function, respectively.You cannot use a formula to specify the lower and upper bounds of the model when you use the
step
orstepwiseglm
function with the name-value pair arguments'Lower'
and'Upper'
, respectively.
Before specifying 'VarNames',varNames
, you can verify the variable
names in varNames
by using the isvarname
function. If the variable names are not valid, then you can
convert them by using the matlab.lang.makeValidName
function.
Example: 'VarNames',{'Horsepower','Acceleration','Model_Year','MPG'}
Data Types: string
| cell
Weights
— Observation weights
ones(n,1)
(default) | n-by-1 vector of nonnegative scalar values
Observation weights, specified as the comma-separated pair consisting
of 'Weights'
and an n-by-1 vector
of nonnegative scalar values, where n is the number
of observations.
Data Types: single
| double
Output Arguments
mdl
— Generalized linear regression model
GeneralizedLinearModel
object
Generalized linear regression model, specified as a GeneralizedLinearModel
object
created using fitglm
or stepwiseglm
.
More About
Terms Matrix
A terms matrix T
is a
t-by-(p + 1) matrix specifying terms in a model,
where t is the number of terms, p is the number of
predictor variables, and +1 accounts for the response variable. The value of
T(i,j)
is the exponent of variable j
in term
i
.
For example, suppose that an input includes three predictor variables x1
,
x2
, and x3
and the response variable
y
in the order x1
, x2
,
x3
, and y
. Each row of T
represents one term:
[0 0 0 0]
— Constant term or intercept[0 1 0 0]
—x2
; equivalently,x1^0 * x2^1 * x3^0
[1 0 1 0]
—x1*x3
[2 0 0 0]
—x1^2
[0 1 2 0]
—x2*(x3^2)
The 0
at the end of each term represents the response variable. In
general, a column vector of zeros in a terms matrix represents the position of the response
variable. If you have the predictor and response variables in a matrix and column vector,
then you must include 0
for the response variable in the last column of
each row.
Formula
A formula for model specification is a character vector or string scalar of
the form '
.y
~
terms
'
y
is the response name.terms
represents the predictor terms in a model using Wilkinson notation.
To represent predictor and response variables, use the variable names of the table
input tbl
or the variable names specified by using
VarNames
. The default value of
VarNames
is
{'x1','x2',...,'xn','y'}
.
For example:
'y ~ x1 + x2 + x3'
specifies a three-variable linear model with intercept.'y ~ x1 + x2 + x3 – 1'
specifies a three-variable linear model without intercept. Note that formulas include a constant (intercept) term by default. To exclude a constant term from the model, you must include–1
in the formula.
A formula includes a constant term unless you explicitly remove the term using
–1
.
Wilkinson Notation
Wilkinson notation describes the terms in a model. The notation relates to the terms included in the model, not to the multipliers (coefficients) of those terms.
Wilkinson notation uses these symbols:
+
means include the next variable.–
means do not include the next variable.:
defines an interaction, which is a product of the terms.*
defines an interaction and all lower order terms.^
raises the predictor to a power, exactly as in*
repeated, so^
includes lower order terms as well.()
groups the terms.
This table shows typical examples of Wilkinson notation.
Wilkinson Notation | Terms in Standard Notation |
---|---|
1 | Constant (intercept) term |
x1^k , where k is a positive
integer | x1 ,
x12 , ...,
x1k |
x1 + x2 | x1 , x2 |
x1*x2 | x1 , x2 ,
x1*x2 |
x1:x2 | x1*x2 only |
–x2 | Do not include x2 |
x1*x2 + x3 | x1 , x2 , x3 ,
x1*x2 |
x1 + x2 + x3 + x1:x2 | x1 , x2 , x3 ,
x1*x2 |
x1*x2*x3 – x1:x2:x3 | x1 , x2 , x3 ,
x1*x2 , x1*x3 ,
x2*x3 |
x1*(x2 + x3) | x1 , x2 , x3 ,
x1*x2 , x1*x3 |
For more details, see Wilkinson Notation.
Canonical Link Function
The default link function for a generalized linear model is the canonical link function.
Distribution | Canonical Link Function Name | Link Function | Mean (Inverse) Function |
---|---|---|---|
'normal' | 'identity' | f(μ) = μ | μ = Xb |
'binomial' | 'logit' | f(μ) = log(μ/(1 – μ)) | μ = exp(Xb) / (1 + exp(Xb)) |
'poisson' | 'log' | f(μ) = log(μ) | μ = exp(Xb) |
'gamma' | -1 | f(μ) = 1/μ | μ = 1/(Xb) |
'inverse gaussian' | -2 | f(μ) = 1/μ2 | μ = (Xb)–1/2 |
Tips
The generalized linear model
mdl
is a standard linear model unless you specify otherwise with theDistribution
name-value pair.For methods such as
plotResiduals
ordevianceTest
, or properties of theGeneralizedLinearModel
object, seeGeneralizedLinearModel
.After training a model, you can generate C/C++ code that predicts responses for new data. Generating C/C++ code requires MATLAB Coder™. For details, see Introduction to Code Generation.
Algorithms
fitglm
calculates the model coefficients using iteratively reweighted least squares (IRLS). If you specify observation weights using theWeights
name-value argument,fitglm
multiplies the weights in the IRLS algorithm by the observation weights.fitglm
treats a categorical predictor as follows:A model with a categorical predictor that has L levels (categories) includes L – 1 indicator variables. The model uses the first category as a reference level, so it does not include the indicator variable for the reference level. If the data type of the categorical predictor is
categorical
, then you can check the order of categories by usingcategories
and reorder the categories by usingreordercats
to customize the reference level. For more details about creating indicator variables, see Automatic Creation of Dummy Variables.fitglm
treats the group of L – 1 indicator variables as a single variable. If you want to treat the indicator variables as distinct predictor variables, create indicator variables manually by usingdummyvar
. Then use the indicator variables, except the one corresponding to the reference level of the categorical variable, when you fit a model. For the categorical predictorX
, if you specify all columns ofdummyvar(X)
and an intercept term as predictors, then the design matrix becomes rank deficient.Interaction terms between a continuous predictor and a categorical predictor with L levels consist of the element-wise product of the L – 1 indicator variables with the continuous predictor.
Interaction terms between two categorical predictors with L and M levels consist of the (L – 1)*(M – 1) indicator variables to include all possible combinations of the two categorical predictor levels.
You cannot specify higher-order terms for a categorical predictor because the square of an indicator is equal to itself.
fitglm
considersNaN
,''
(empty character vector),""
(empty string),<missing>
, and<undefined>
values intbl
,X
, andY
to be missing values.fitglm
does not use observations with missing values in the fit. TheObservationInfo
property of a fitted model indicates whether or notfitglm
uses each observation in the fit.
Alternative Functionality
Use
stepwiseglm
to select a model specification automatically. Usestep
,addTerms
, orremoveTerms
to adjust a fitted model.
References
[1] Collett, D. Modeling Binary Data. New York: Chapman & Hall, 2002.
[2] Dobson, A. J. An Introduction to Generalized Linear Models. New York: Chapman & Hall, 1990.
[3] McCullagh, P., and J. A. Nelder. Generalized Linear Models. New York: Chapman & Hall, 1990.
Extended Capabilities
Tall Arrays
Calculate with arrays that have more rows than fit in memory.
This function supports tall arrays for out-of-memory data with some limitations.
If any input argument to
fitglm
is a tall array, then all of the other inputs must be tall arrays as well. This includes nonempty variables supplied with the'Weights'
,'Exclude'
,'Offset'
, and'BinomialSize'
name-value pairs.You cannot specify the
LikelihoodPenalty
name-value argument.The default number of iterations is 5. You can change the number of iterations using the
'Options'
name-value pair to pass in an options structure. Create an options structure usingstatset
to specify a different value forMaxIter
.For tall data,
fitglm
returns aCompactGeneralizedLinearModel
object that contains most of the same properties as aGeneralizedLinearModel
object. The main difference is that the compact object is sensitive to memory requirements. The compact object does not include properties that include the data, or that include an array of the same size as the data. The compact object does not contain theseGeneralizedLinearModel
properties:Diagnostics
Fitted
Offset
ObservationInfo
ObservationNames
Residuals
Steps
Variables
You can compute the residuals directly from the compact object returned by
GLM = fitglm(X,Y)
usingRES = Y - predict(GLM,X); S = sqrt(GLM.SSE/GLM.DFE); histogram(RES,linspace(-3*S,3*S,51))
For more information, see Tall Arrays for Out-of-Memory Data.
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Version History
Introduced in R2013bR2024a: Specify penalized likelihood estimation
fitglm
now supports penalized likelihood estimation by
Jeffreys prior. You can use Jeffreys prior to reduce the coefficient estimate bias when
fitting a generalized linear regression model to a separable data set or small number of
samples. To penalize the likelihood estimate, set the LikelihoodPenalty
name-value argument to "jeffreys-prior"
.
MATLAB Command
You clicked a link that corresponds to this MATLAB command:
Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list:
How to Get Best Site Performance
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)