Log linear, logit and probit models are particular cases of general linear models.
Log linear analysis deals with the correlation of the categorical type of variables. Log linear analysis observes all possible levels of main and interaction effects, and then compares the saturated model with the reduced model. The major purpose of log linear analysis is to obtain the most parsimonious model. The other name for log linear analysis is multi way frequency analysis (MFA). Log linear analysis is an independent procedure that is used to account for the distribution of cases in a joint distribution or cross tabulation of the categorical variables.
Logit analysis is similar to log linear analysis, except that logit analysis deals with one or more categorical types of dependent variables.
Probit analysis is done when the categories of the variables are assumed to reflect an underlying normal distribution of the dependent variables. Probit analysis can be done even with the variables having only two categories.
In log linear analysis, log linear models have been developed to analyze the conditional association between two or more categorical variables.
The logit and the probit analysis allow the log linear model to expand by allowing the mixture of the categorical and continuous independent variables to assume one or more categorical dependent variables.
There are two different types of log linear procedures: Hierarchical log linear procedure and General log linear procedure.
There are certain things that one should keep in mind while working with Log linear, logit and probit models.
In the log linear kind of analysis, the variables may be factors, covariates, contrasts, etc. but the two different types of log linear procedures support all types of variables.
In probit analysis, the levels of the factors are used to explain the subgroup during the analysis.
The saturated model in log linear analysis is a kind of model that incorporates all the possible effects, such as one way effect, two way interactions effects, three way interactions, etc. A saturated model in log linear analysis forces absolutely no constraints on the data. This model in log linear analysis always replicates the observed frequencies.
The parsimonious models in log linear analysis are incomplete models that somehow achieve a satisfactory level of goodness of fit.
There are certain assumptions of Log linear, logit and probit models.
In the case of log linear analysis, well populated tables are being assumed.
The well populated tables in Log linear, logit and probit models require an adequate number in their sample size.
Also, it should be noted by the researcher that both the logit and probit models utilize maximum likelihood estimation, which assumes a larger sample size.
A general rule to follow is that the sample size in Log linear, logit and probit models should be at least five times the number of cells in the tables.
The residuals are generally smaller in Log linear, logit and probit models so that no large outliers are present in the cell.
The residuals in Log linear, logit and probit models are assumed to be normally distributed.
The observations in Log linear, logit and probit models are always assumed to be independent.
