# science + socst, family = binomial(), data = hsb) # Call: glm(formula = I(prog = "academic") ~ ses + schtyp + read + write + # I(prog = "academic") ~ ses + schtyp + read + write + science + # I(prog = "academic") ~ gender + ses + schtyp + read + write +
# I(prog = "academic") ~ gender + race + ses + schtyp + read + Instead, we will use step() with the criteria being the LRT to reduce unneeded variables from the model.Įnter the following command in your script and run it. Under asymptotic conditions the deviance is expected to be \(\chi^2_\) distributed. The deviance can be used for this goodness of fit check. This relationship can be used to evaluate the model’s goodness of fit to the data. GLM models have a defined relationship between the expected variance and the mean. The decision of which family is appropriate is not discussed in this series. This would be specified as family = quasipoisson(link = "identity") For example, if the response variable is non negative and the variance is proportional to the mean, you would use the “identity” link with the “quasipoisson” family function. The default link function for a family can be changed by specifying a link to the family function. The quasi families allows inference to be done when your data is overdispersed or underdispersed, provided that the variance is proportional. This results in a variance function of \(\alpha\mu\) instead of \(1\mu\) as for Poisson distributed data. This would use the “quasipoisson” family. An example would be data in which the variance is proportional to the mean. This is done with quasi families, where Pearson’s \(\chi^2\) (“chi-squared”) is used to scale the variance. GLM models can also be used to fit data in which the variance is proportional to one of the defined variance functions. A GLM model is defined by both the formula and the family. As an example the “poisson” family uses the “log” link function and “ \(\mu\)” as the variance function. In R, a family specifies the variance and link functions which are used in the model fit. The variance function specifies the relationship of the variance to the mean. This transformation of the response may constrain the range of the response variable. The transformation done on the response variable is defined by the link function. GLM models transform the response variable to allow the fit to be done by least squares. GLMs are useful when the range of your response variable is constrained and/or the variance is not constant or normally distributed.
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