Ignoring the ordinal categories of the The Ordered Logit Model (OLM) variable and treating it as nomial, i.e. us MNLM. The key problem is a loss of Say Y is an ordinal dependent variable efficiency By ignoring the fact that the with c categories. Let Pr(Y sj)denote the ategories are ordered, you fail to use probability that the response on Y falls in some of the information available to you, category j or below(i.e, in category and you may estimate many more 1, 2, .. or j). This is called a cumulative parameters than is necessary. This probability. It equals the sum of the increases the risk of getting insignificant probabilities in category j and below results, but your parameter estimates still should be unbiased Pr(Y sil=PrY=1)+伊Pr(Y=2)+… +Pr(Y=j) Data type A"c category Y dependent variable"has c cumulative probabilities: Pr(Y $1), Pr(Ys As in other logistic regression, the 2), Pr(Y sc). The final cumulative predictors in ordinal logistic regression probability uses the entire scale; as a may be quantitative, categorical, or a consequence, therefore Pr(Y sc)=1 mixture of the two. The dependent variable The order of forming the final cumulative should be discrete and ordinal with three probabilities reflects the ordering or more categones dependent variable scale, and those probabilities themselves satisfy In SPSS, discrete(categorical) variables are entered as factors and continuous PrYs1)sPr(YS2)≤S∴≤ Pr(Y sc)=1 variables as covariates3 5 • Ignoring the ordinal categories of the variable and treating it as nomial, i.e. use MNLM. The key problem is a loss of efficiency. By ignoring the fact that the categories are ordered, you fail to use some of the information available to you, and you may estimate many more parameters than is necessary. This increases the risk of getting insignificant results, but your parameter estimates still should be unbiased. 6 Data type • As in other logistic regression, the predictors in ordinal logistic regression may be quantitative, categorical, or a mixture of the two. The dependent variable should be discrete and ordinal with three or more categories. • In SPSS, discrete (categorical) variables are entered as factors, and continuous variables as covariates. 4 7 The Ordered Logit Model (OLM) • Say Y is an ordinal dependent variable with c categories. Let Pr(Y ≤ j) denote the probability that the response on Y falls in category j or below (i.e., in category 1,2, …, or j). This is called a cumulative probability. It equals the sum of the probabilities in category j and below: Pr(Y ≤ j)= Pr(Y = 1) + (Pr(Y = 2)+ … +Pr(Y = j) 8 • A “ c category Y dependent variable” has c cumulative probabilities: Pr(Y ≤ 1), Pr(Y ≤ 2), … Pr(Y ≤ c). The final cumulative probability uses the entire scale; as a consequence, therefore, Pr(Y ≤ c) = 1. The order of forming the final cumulative probabilities reflects the ordering of the dependent variable scale, and those probabilities themselves satisfy: Pr(Y ≤ 1) ≤ Pr(Y ≤ 2) ≤ … ≤ Pr(Y ≤ c) = 1