Applied Ordinal Logistic Regression Using Stata by xing liu

Author:xing liu
Language: eng
Format: epub
Published: 2018-06-23T16:00:00+00:00

Interpreting the Output

The transition tree is displayed at the beginning of the output. The three transitional points include transitions from category 1 to categories 2 through 4, from category 2 to categories 3 and 4, and from categories 3 to 4. The log likelihood value, the number of observations, the log likelihood ratio test statistic, and the associated p value are reported next.

At the bottom of the output, the regression coefficient table for the fitted model displays the parameter estimates, standard errors, Wald z statistics, associated p values, and the 95% confident intervals of the parameter estimates. This table includes three subsections. Each section displays the parameter estimates for an underlying binary logistic model, which reflects the category comparison specified in the transition tree. The first binary model estimates the logit or log odds of being in categories 2, 3, and 4 versus 1; the second model estimates the logit of being in categories 3 and 4 versus 2; and the third model estimates the logit of being in category 4 versus 3. In other words, these three binary models estimate the logit or log odds of being above a particular category versus being in that category.

The logit coefficient table here looks similar to that of the generalized ordinal logistic regression model introduced in Chapter 5 since the logit coefficients of all predictor variables are allowed to vary freely across the underlying binary models. For example, the estimated logit coefficients for maritals are .472, .455, and .491 for each binary model. Therefore, the estimated sequential logit model in this example is called the unconstrained continuation ratio model. If an ordinal response variable has J levels in an unconstrained continuation ratio model, we need to estimate J − 1 logit coefficients for each predictor variable. A more parsimonious model is the constrained continuation ratio model where the logit coefficients for each predictor variable are constrained to be equal across the underlying binary comparisons. The CR model introduced in the preceding sections is the constrained model, which is the focus in this chapter. Similar to the PO model, the logit coefficients for each predictor variable are assumed to be equal in the constrained CR model.

How can we fit the same CR model introduced earlier in this chapter using the seqlogit command? In other words, how can we fit the constrained CR model? To replicate the results previously estimated by the ocratio command, we need to constrain the logit coefficients for each predictor to be equal across the three binary logistic regression models with the constraint option in the seqlogit command syntax. Before executing the seqlogit command, we also need to use the constraint define command or constraint to define eight constraints, with two for each predictor variable. The total number of constraints is determined by both the number of predictor variables and the number of transitions or comparisons in the transition tree. See Chapter 7 for more details on how to use the constraint command.

The command for the first constraint [_2_3_4v1]1. maritals = [_3_4v2]1.

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