# Ordered logistic regression (and similar models)

With SPSS procedure PLUM (available in versions 10 or higher), you may estimate the influence of variables on a dependent variable with several ordered categories (such as "agree strongly", "agree somewhat", "neither - nor", "disagree somewhat", "disagree strongly", or, in a physician's judgment of a patient's condition, "improved", "no change", "worsened"). I hope later versions of this guide will explain a little bit more in detail what these models -- developed more than 25 years ago, but still less than well-known among social scientists -- are all about, but for the moment I will only present and briefly comment two examples.

*Simple example*

PLUM judgment WITH age BY treatmnt | |

/ PRINT FIT PARAMETER SUMMARY. |

*More complex example*

PLUM judgment WITH age BY treatmnt | |

/ LINK CLOGLOG | |

/ LOCATION = age treatment age*treatmnt | |

/ PRINT FIT PARAMETER SUMMARY TPARALLEL | |

/ SAVE = ESTPROB PREDCAT PCPROB ACPROB. |

In the *simple example*, a variable judgment (for instance, a physician's judgment of the condition of a patient) is regressed on a metric variable, age (hence keyword WITH) and a categorical variable treatmnt (i.e. treatment) (hence keyword BY). Note that the very useful keyword CONTRAST, available in procedures such as LOGISTIC REGRESSION or COXREG, cannot be used here. Rather, the last category of the categorical variable is used as a reference category. Therefore, you are advised to code (or recode) your categorical variables according to your needs.

In the *complex example*, several options are indicated. First, instead of the default logit link, a cumulative log-log link is requested (other links are CAUCHIT, NLOGLOG and PROBIT). Subcommand LOCATION permits to specificy interaction effects (here between age and treatment). In the PRINT subcommand, in addition to the usual output, a test of parallelity of slopes is requested (note that as any other test, this test is affected by your sample size; with large samples, the null hypothesis of parallel slopes almost always will be rejected). Finally, several statistics about actual and estimated categories and probabilities can be obtained with the SAVE command: ESTPROB will compute, for each category of the dependent variable, the estimated probability (that is, with three categories, you will get three new variables); PREDCAT will save the in a single variable the category each subject falls into as predicted by the model (this is the category with the highest probability); PCPROB is a single variable indicating the probability of PREDCAT (this is the probability of ESTPROB pertaining to the category with the highest probability); and ACPROB, the probability (according to the model) of the category each subject actually belongs to.

© W. Ludwig-Mayerhofer, IGSW | Last update: 26 Jul 2002