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stepwiseglm
Create generalized linear regression model by stepwise regression
Sintaxis
mdl = stepwiseglm(tbl,modelspec)mdl = stepwiseglm(X,y,modelspec)mdl = stepwiseglm(...,modelspec,Name,Value)Descripción
mdl = stepwiseglm(...,modelspec,Name,Value)Name,Value pair arguments.
Ejemplos
Generalized Linear Model Using Stepwise Algorithm
Create response data using just three of 20 predictors, and create a generalized linear model using stepwise algorithm to see if it uses just the correct predictors.
Create data with 20 predictors, and Poisson response using just three of the predictors, plus a constant.
rng('default') % for reproducibility X = randn(100,20); mu = exp(X(:,[5 10 15])*[.4;.2;.3] + 1); y = poissrnd(mu);
Fit a generalized linear model using the Poisson distribution.
mdl = stepwiseglm(X,y,... 'constant','upper','linear','Distribution','poisson')
1. Adding x5, Deviance = 134.439, Chi2Stat = 52.24814, PValue = 4.891229e-13 2. Adding x15, Deviance = 106.285, Chi2Stat = 28.15393, PValue = 1.1204e-07 3. Adding x10, Deviance = 95.0207, Chi2Stat = 11.2644, PValue = 0.000790094
mdl =
Generalized linear regression model:
log(y) ~ 1 + x5 + x10 + x15
Distribution = Poisson
Estimated Coefficients:
Estimate SE tStat pValue
________ ________ ______ __________
(Intercept) 1.0115 0.064275 15.737 8.4217e-56
x5 0.39508 0.066665 5.9263 3.0977e-09
x10 0.18863 0.05534 3.4085 0.0006532
x15 0.29295 0.053269 5.4995 3.8089e-08
100 observations, 96 error degrees of freedom
Dispersion: 1
Chi^2-statistic vs. constant model: 91.7, p-value = 9.61e-20
The starting model is the constant model. stepwiseglm by default uses deviance of the model as the criterion. It first adds x5 into the model, as the 
-value for the test statistic, deviance (the differences in the deviances of the two models), is less than the default threshold value 0.05. Then, it adds x15 because given x5 is in the model, when x15 is added, the 
-value for chi-squared test is smaller than 0.05. It then adds x10 because given x5 and x15 are in the model, when x10 is added, the 
-value for the chi-square test statistic is again less than 0.05.
Argumentos de entrada
Output Arguments
Más acerca de
Sugerencias
The generalized linear model
mdlis a standard linear model unless you specify otherwise with theDistributionname-value pair.For other methods such as
devianceTest, or properties of theGeneralizedLinearModelobject, 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.
Algoritmos
Stepwise regression is a systematic method
for adding and removing terms from a linear or generalized linear
model based on their statistical significance in explaining the response
variable. The method begins with an initial model, specified using modelspec,
and then compares the explanatory power of incrementally larger and
smaller models.
MATLAB uses forward and backward stepwise regression to
determine a final model. At each step, the method searches for terms
to add to or remove from the model based on the value of the 'Criterion' argument.
The default value of 'Criterion' is 'sse',
and in this case, stepwiselm uses the p-value
of an F-statistic to test models with and without
a potential term at each step. If a term is not currently in the model,
the null hypothesis is that the term would have a zero coefficient
if added to the model. If there is sufficient evidence to reject the
null hypothesis, the term is added to the model. Conversely, if a
term is currently in the model, the null hypothesis is that the term
has a zero coefficient. If there is insufficient evidence to reject
the null hypothesis, the term is removed from the model.
Here is how stepwise proceeds when 'Criterion' is 'sse':
Fit the initial model.
Examine a set of available terms not in the model. If any of these terms have p-values less than an entrance tolerance (that is, if it is unlikely that they would have zero coefficient if added to the model), add the one with the smallest p-value and repeat this step; otherwise, go to step 3.
If any of the available terms in the model have p-values greater than an exit tolerance (that is, the hypothesis of a zero coefficient cannot be rejected), remove the one with the largest p-value and go to step 2; otherwise, end.
At any stage, the function will not add a higher-order term
if the model does not also include all lower-order terms that are
subsets of it. For example, it will not try to add the term X1:X2^2 unless
both X1 and X2^2 are already
in the model. Similarly, the function will not remove lower-order
terms that are subsets of higher-order terms that remain in the model.
For example, it will not examine to remove X1 or X2^2 if X1:X2^2 stays
in the model.
The default for stepwiseglm is 'Deviance' and
it follows a similar procedure for adding or removing terms.
There are several other criteria available, which you can specify
using the 'Criterion' argument. You can use the
change in the value of the Akaike information criterion, Bayesian
information criterion, R-squared, adjusted R-squared as a criterion
to add or remove terms.
Depending on the terms included in the initial model and the order in which terms are moved in and out, the method might build different models from the same set of potential terms. The method terminates when no single step improves the model. There is no guarantee, however, that a different initial model or a different sequence of steps will not lead to a better fit. In this sense, stepwise models are locally optimal, but might not be globally optimal.
Alternatives
Use fitglm to create a
model with a fixed specification. Use step, addTerms,
or removeTerms to adjust a fitted model.
Referencias
[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.
Consulte también
Introducido en R2013b
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