Overview (LOGLINEAR command)

LOGLINEAR is a general procedure for model fitting, hypothesis testing, and parameter estimation for any model that has categorical variables as its major components. As such, LOGLINEAR subsumes a variety of related techniques, including general models of multiway contingency tables, logit models, logistic regression on categorical variables, and quasi-independence models.

LOGLINEAR models cell frequencies using the multinomial response model and produces maximum likelihood estimates of parameters by means of the Newton-Raphson algorithm 1. HILOGLINEAR, which uses an iterative proportional-fitting algorithm, is more efficient for hierarchical models, but it cannot produce parameter estimates for unsaturated models, does not permit specification of contrasts for parameters, and does not display a correlation matrix of the parameter estimates.

Comparison of the GENLOG and LOGLINEAR Commands

The General Loglinear Analysis and Logit Loglinear Analysis dialog boxes are both associated with the GENLOG command. In previous releases, these dialog boxes were associated with the LOGLINEAR command. The LOGLINEAR command is now available only as a syntax command. The differences are described below.

Distribution Assumptions

  • GENLOG can handle both Poisson and multinomial distribution assumptions for observed cell counts.
  • LOGLINEAR assumes only multinomial distribution.

Approach

  • GENLOG uses a regression approach to parameterize a categorical variable in a design matrix.
  • LOGLINEAR uses contrasts to reparameterize a categorical variable. The major disadvantage of the reparameterization approach is in the interpretation of the results when there is a redundancy in the corresponding design matrix. Also, the reparameterization approach may result in incorrect degrees of freedom for an incomplete table, leading to incorrect analysis results.

Contrasts and Generalized Log-Odds Ratios (GLOR)

  • GENLOG doesn’t provide contrasts to reparameterize the categories of a factor. However, it offers generalized log-odds ratios (GLOR) for cell combinations. Often, comparisons among categories of factors can be derived from GLOR.
  • LOGLINEAR offers contrasts to reparameterize the categories of a factor.

Deviance Residual

  • GENLOG calculates and displays the deviance residual and its normal probability plot in addition to the other residuals.
  • LOGLINEAR does not calculate the deviance residual.

Factor-by-Covariate Design

  • When there is a factor-by-covariate term in the design, GENLOG generates one regression coefficient of the covariate for each combination of factor values. The estimates of these regression coefficients are calculated and displayed.
  • LOGLINEAR estimates and displays the contrasts of these regression coefficients.

Partition Effect

  • In GENLOG, the term partition effect refers to the category of a factor.
  • In LOGLINEAR, the term partition effect refers to a particular contrast.

Options

Model Specification. You can specify the model or models to be fit using the DESIGN subcommand.

Cell Weights. You can specify cell weights, such as structural zeros, for the model with the CWEIGHT subcommand.

Output Display. You can control the output display with the PRINT subcommand.

Optional Plots. You can produce plots of adjusted residuals against observed and expected counts, normal plots, and detrended normal plots with the PLOT subcommand.

Linear Combinations. You can calculate linear combinations of observed cell frequencies, expected cell frequencies, and adjusted residuals using the GRESID subcommand.

Contrasts. You can indicate the type of contrast desired for a factor using the CONTRAST subcommand.

Criteria for Algorithm. You can control the values of algorithm-tuning parameters with the CRITERIA subcommand.

Basic Specification

The basic specification is two or more variables that define the crosstabulation. The minimum and maximum values for each variable must be specified in parentheses after the variable name.

By default, LOGLINEAR estimates the saturated model for a multidimensional table. Output includes the factors or effects, their levels, and any labels; observed and expected frequencies and percentages for each factor and code; residuals, standardized residuals, and adjusted residuals; two goodness-of-fit statistics (the likelihood-ratio chi-square and Pearson’s chi-square); and estimates of the parameters with accompanying z values and 95% confidence intervals.

Limitations

  • A maximum of 10 independent (factor) variables
  • A maximum of 200 covariates

Subcommand Order

  • The variables specification must come first.
  • The subcommands that affect a specific model must be placed before the DESIGN subcommand specifying the model.
  • All subcommands can be used more than once and, with the exception of the DESIGN subcommand, are carried from model to model unless explicitly overridden.
  • If the last subcommand is not DESIGN, LOGLINEAR generates a saturated model in addition to the explicitly requested model(s).
1 Haberman, S. J. 1978. Analysis of qualitative data. London: Academic Press.