CH6-4 - Outline Chapter 6. Building and Applying Logistic...

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Chapter 6. Building and Applying Logistic Regression Models Deyuan Li School of Management, Fudan University Feb. 28, 2011 1/65 Outline 6.1 Strategies in Model Selection 6.2 Logistic Regression Diagnostics 6.3 Inference about Conditional Association in 2 ×× K Tables 2/65 6.1 Strategies in model selection The selection process becomes harder as the number of explanatory variables increases, because of the rapid increase in possible e±ects and interactions. Two competing goals of model selection: the model should be complex enough to ²t the data well; the model should be simple to interpret, smoothing rather than over²tting the data. Most models are designed to answer certain questions. Those questions guide the choice of model terms: Confrmatory analysis use a restrict set of models; e.g., a study hypothesis about an e±ect may be tested by comparing models with and without that e±ect. For exploratory studies, a search among possible models may provide clues about the dependence structure and raise questions for future research. 3/65 In either case, it is helpful ²rst to study the e±ect on Y of each predictor by itself using graphics (incorporating smoothing) for a continuous predictor or a contingency table for a discrete predictor. This give a “feel” for the marginal e±ects. Unbalanced data, with relatively few responses of one type, limit the number of explanatory variables ( x terms) for the model. One guideline: at least 10 outcomes of each type should occur for every x term. For instance, if y = 1 only 30 times out of n = 1000, the model should contain no more than about 3 x terms. Such guidelines are approximate. This does not mean that if you have 500 outcomes of each type you are well served by a model with 50 x terms. 4/65
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Many model selection procedures exist, no one of which is always best. A model with several predictors may suFer from multicollinearity , i.e., correlations among predictors making it seem that no one predictor is important when all the others are in the model. A predictor may seem to have little eFect because it overlaps considerably with other predictors in the model, i.e., itself being predicted well by the other predictors. Deleting such a redundant predictor can be helpful, for instance to reduce standard errors of other estimated eFects. 5/65 6.1.1 Horseshoe crab example revisited The horseshoe crab data set in Table 4.3 has four predictors: color (4 categories), spine condition (3 categories), weight and width of the carapace shell. Outcome: The crab has satellites ( y = 1) or not ( y =0) . Preliminary model: 4 predictors, only main eFects logit[ P ( Y =1)] = α + β 1 weight + β 2 width + β 3 c 1 + β 4 c 2 + β 5 c 3 + β 6 s 1 + β 7 s 2 , treating color ( c i ) and spine condition ( s j ) as qualitative (factors), with dummy variables for the ±rst 3 colors and the ±rst 2 spine conditions. Table 6.1 shows results.
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This note was uploaded on 11/20/2011 for the course ST 3241 taught by Professor Deyuanli during the Spring '11 term at Adams State University.

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CH6-4 - Outline Chapter 6. Building and Applying Logistic...

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