# Cal Poly STAT 418 - Multicategory Logit Models (4 pages)

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## Multicategory Logit Models

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## Multicategory Logit Models

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Lecture Notes

Pages:
4
School:
California Polytechnic State University
Course:
Stat 418 - Categorical Data Analysis
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Winter 2014 Wednesday Feb 12 Stat 418 Day 21 Multicategory Logit Models Ch 6 Don t forget about initial graphical explorations of the data Prediction tables Confusion matrix can be a useful way to summarize the predictive power of a logistic regression model correct classification rate o May want to try difference choices of cut off value o May want to balance sensitivity probability of correct prediction of success and specificity probability of correct prediction of failure ROC curves summarizes predictive power for all possible cut off values o Area under curve concordance index what proportion of pairs with one success and one failure estimated a higher probability for the success Example 1 Suppose a business wants to predict a firm s commitment of resources to total quality management large moderate small from size of firm type of industry and several other explanatory variables Or a researcher wants to predict the severity of disease mild moderate severe based on age of patient gender of patient and other explanatory variables Or you want to predict students mode of transportation to school car walking bicycle bus and how this choice is related to age sex distance etc a What is the main difference in these research questions and what we have examined before b What is a key distinction between the last two examples So we want a model of the form P Yi k eX 1 eX for k 1 J One approach is rather than only comparing P Yi k to 1 P Yi k we can compare P Y k to P Y m If we choose one response category as the baseline then we can set up J 1 logit functions log i J 0i 1i x1 2i x 2 You could of course just fit pairs of categories separately but fitting the multicategory logits simultaneously will generally have smaller standard errors and allows for analyses to adjust for the effects of the other variables Also you will be able to test whether a predictor or set of predictors is useful across the levels of the response rather than just in a specific pair Example 2 Hosmer

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