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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 effects and interactions. Two competing goals of model selection: the model should be complex enough to fit the data well; the model should be simple to interpret, smoothing rather than overfitting the data. Most models are designed to answer certain questions. Those questions guide the choice of model terms: Confirmatory analysis use a restrict set of models; e.g., a study hypothesis about an effect may be tested by comparing models with and without that effect. 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 first to study the effect 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 effects. 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 suffer 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 effect 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 effects. 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 effects 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 first 3 colors and the first 2 spine conditions. Table 6.1 shows results.
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