Generalized linear model regression
b = glmfit(X,y,
distr
)
b = glmfit(X,y,distr
,param1
,val1
,param2
,val2
,...)
[b,dev] = glmfit(...)
[b,dev,stats] = glmfit(...)
b = glmfit(X,y,
returns
a (p + 1)by1 vector distr
)b
of coefficient
estimates for a generalized linear regression of the responses in y
on
the predictors in X
, using the distribution
. distr
X
is
an nbyp matrix of p predictors
at each of n observations. distr
can
be any of the following: 'binomial'
, 'gamma'
, 'inverse
gaussian'
, 'normal'
(the default), and 'poisson'
.
In most cases, y
is an nby1
vector of observed responses. For the binomial distribution, y
can
be a binary vector indicating success or failure at each observation,
or a two column matrix with the first column indicating the number
of successes for each observation and the second column indicating
the number of trials for each observation.
This syntax uses the canonical link (see below) to relate the distribution to the predictors.
Note
By default, glmfit
adds a first column of
1s to X
, corresponding to a constant term in the
model. Do not enter a column of 1s directly into X
.
You can change the default behavior of glmfit
using
the 'constant'
parameter, below.
glmfit
treats NaN
s in
either X
or y
as missing values,
and ignores them.
b = glmfit(X,y,
additionally
allows you to specify optional parameter name/value pairs to control
the model fit. Acceptable parameters are as follows.distr
,param1
,val1
,param2
,val2
,...)
Parameter  Value  Description 

'link' 
 µ = Xb 
 log(µ) = Xb  
 log(µ/(1 – µ)) = Xb  
'probit' 
 
'comploglog'  log( log(1 – µ)) = Xb  
'reciprocal' , default for the distribution 'gamma'  1/µ = Xb  
 log( log(µ)) = Xb  
 µ^{p} = Xb  
cell array of the form  Customdefined link function. You must provide
 
structure array having these fields:
The value of each field is a character vector corresponding
to a function that is on the path or a function handle (created using  Customdefined link function, its derivative, and its inverse.  
'estdisp'  'on' 


 
'offset'  Vector 

'weights'  Vector of prior weights, such as the inverses of the relative variance of each observation  
'constant' 


'off' 

[b,dev] = glmfit(...)
returns
dev
, the deviance of the fit at the solution vector. The deviance is a
generalization of the residual sum of squares. It is possible to perform an analysis of deviance
to compare several models, each a subset of the other, and to test whether the model with more
terms is significantly better than the model with fewer terms.
[b,dev,stats] = glmfit(...)
returns dev
and stats
.
stats
is a structure with the following fields:
beta
— Coefficient estimates b
dfe
— Degrees of freedom
for error
sfit
— Estimated dispersion
parameter
s
— Theoretical or estimated
dispersion parameter
estdisp
— 0 when the 'estdisp'
namevalue
pair argument value is 'off'
and 1 when the 'estdisp'
namevalue
pair argument value is 'on'
.
covb
— Estimated covariance
matrix for B
se
— Vector of standard
errors of the coefficient estimates b
coeffcorr
— Correlation
matrix for b
t
— t statistics
for b
p
— pvalues
for b
resid
— Vector of residuals
residp
— Vector of Pearson
residuals
residd
— Vector of deviance
residuals
resida
— Vector of Anscombe
residuals
If you estimate a dispersion parameter for the binomial or Poisson
distribution, then stats.s
is set equal to stats.sfit
.
Also, the elements of stats.se
differ by the factor stats.s
from
their theoretical values.
[1] Dobson, A. J. An Introduction to Generalized Linear Models. New York: Chapman & Hall, 1990.
[2] McCullagh, P., and J. A. Nelder. Generalized Linear Models. New York: Chapman & Hall, 1990.
[3] Collett, D. Modeling Binary Data. New York: Chapman & Hall, 2002.
fitglm
 GeneralizedLinearModel
 glmval
 regress
 regstats
 stepwiseglm