Overview (HILOGLINEAR command)

HILOGLINEAR fits hierarchical loglinear models to multidimensional contingency tables using an iterative proportional-fitting algorithm. HILOGLINEAR also estimates parameters for saturated models. These techniques are described elsewhere in 1, 2, and 3. HILOGLINEAR is much more efficient for these models than the LOGLINEAR procedure because HILOGLINEAR uses an iterative proportional-fitting algorithm rather than the Newton-Raphson method used in LOGLINEAR.

Options

Design Specification. You can request automatic model selection using backward elimination with the METHOD subcommand. You can also specify any hierarchical design and request multiple designs using the DESIGN subcommand.

Design Control. You can control the criteria used in the iterative proportional-fitting and model-selection routines with the CRITERIA subcommand. You can also limit the order of effects in the model with the MAXORDER subcommand and specify structural zeros for cells in the tables you analyze with the CWEIGHT subcommand.

Display and Plots. You can select the display for each design with the PRINT subcommand. For saturated models, you can request tests for different orders of effects as well. With the PLOT subcommand, you can request residuals plots or normal probability plots of residuals.

Basic Specification

  • The basic specification is a variable list with at least two variables followed by their minimum and maximum values.
  • HILOGLINEAR estimates a saturated model for all variables in the analysis.
  • By default, HILOGLINEAR displays parameter estimates, measures of partial association, goodness of fit, and frequencies for the saturated model.

Subcommand Order

  • The variable list must be specified first.
  • Subcommands affecting a given DESIGN must appear before the DESIGN subcommand. Otherwise, subcommands can appear in any order.
  • MISSING can be placed anywhere after the variable list.

Syntax Rules

  • DESIGN is optional. If DESIGN is omitted or the last specification is not a DESIGN subcommand, a default saturated model is estimated.
  • You can specify multiple PRINT, PLOT, CRITERIA, MAXORDER, and CWEIGHT subcommands. The last of each type specified is in effect for subsequent designs.
  • PRINT, PLOT, CRITERIA, MAXORDER, and CWEIGHT specifications remain in effect until they are overridden by new specifications on these subcommands.
  • You can specify multiple METHOD subcommands, but each one affects only the next design.
  • MISSING can be specified only once.

Operations

  • HILOGLINEAR builds a contingency table using all variables on the variable list. The table contains a cell for each possible combination of values within the range specified for each variable.
  • HILOGLINEAR assumes that there is a category for every integer value in the range of each variable. Empty categories waste space and can cause computational problems. If there are empty categories, use the RECODE command to create consecutive integer values for categories.
  • Cases with values outside the range specified for a variable are excluded.
  • If the last subcommand is not a DESIGN subcommand, HILOGLINEAR displays a warning and generates the default model. This is the saturated model unless MAXORDER is specified. This model is in addition to any that are explicitly requested.
  • If the model is not saturated (for example, when MAXORDER is less than the number of factors), only the goodness of fit and the observed and expected frequencies are given.
  • The display uses the WIDTH subcommand defined on the SET command. If the defined width is less than 132, some portions of the display may be deleted.

Limitations

The HILOGLINEAR procedure cannot estimate all possible frequency models, and it produces limited output for unsaturated models.

  • It can estimate only hierarchical loglinear models.
  • It treats all table variables as nominal. (You can use LOGLINEAR to fit nonhierarchical models to tables involving variables that are ordinal.)
  • It can produce parameter estimates for saturated models only (those with all possible main-effect and interaction terms).
  • It can estimate partial associations for saturated models only.
  • It can handle tables with no more than 10 factors.
1 Everitt, B. S. 1977. The Analysis of Contingency Tables. London: Chapman & Hall.
2 Bishop, Y. M., S. E. Feinberg, and P. W. Holland. 1975. Discrete multivariate analysis: Theory and practice. Cambridge, Mass.: MIT Press.
3 Goodman, L. A. 1978. Analyzing qualitative/categorical data. New York: University Press of America.