Multinomial logistic regression models and ordinal variables

The multinomial (aka polytomous) logistic regression is a simple extension of binomial logistic regression model. They are used when the dependent variable is greater than two (disordered) has rated categories.

Dummy coding of independent variables is quite common. In multinomial logistic regression the dependent variable is coded in several dummy 1 / 0 variables. This is a variable for all categories except one, so if there are categories M, M-1 dummyVariables. All except their own category dummy variable. Each category is dummy variable has a value of 1 in its category and a 0 for all others. A category, the category of reference, is not its own dummy variable, as is clearly indicated by all other variables equal to 0.

Logistic regression mulitnomial then estimated a separate binary logistic regression model for each of these dummy variables. The result is M-1 binary logistic regression models. Each tells theEffects of predictors on the probability of success in this category compared to the reference category. Each model has its own intercept and regression coefficients - the predictors may be of interest to each class may vary.

Why not just run a series of binary regression models? They could, and people were once, in multinomial regression models in the software away. You will probably get similar results. But they run together means that they estimated simultaneously,that the parameter estimates are more efficient - there are fewer errors unexplained.

Ordinal Logistic Regression: Proportional Odds Model

If the response categories are ordered, you could have a multinomial regression model. The disadvantage is that you throw away the information about the order. An ordinal logistic regression model retains this information, it is more complicated.

In the proportional odds model, the event modelnot with a score in a single category, as in the binary and multinomial models. Rather, the event is modeled with a score in a particular category or all of the previous category.

For example, for a response variable with three ordered categories, the possible events, defined as:

* In Group 1
* In Group 2, or 1
* In Group 3, 2 or 1

In the proportional odds model, each trap has its output, but the same regressionCoefficients. This means:

1. the overall rate of all cases, be different, but according to the effect of predictors on the probability of an event in any other category, for each category. This is a hypothesis of the model, you need to check. It is often violated.

The model is a bit 'different than usual, written in SPSS, with a hyphen between the intercept and all coefficients of regression. This is a convention to ensure that, for positive coefficients,Increases the values of X lead to an increased likelihood of a greater number of response categories. In SAS, the character is a plus, and elevations of a predictor for increased risk of lead lower numbered response categories. Make sure you understand how the model in your statistics package before interpreting the results.