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6b_multinomial logistic

# 6b_multinomial logistic - What is Multinomial Logistic...

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1 Advanced Topics in Forest Biometrics FOR6934 Multinomial Logistic Regression What is Multinomial Logistic Regression? A form of logistic regression for predicting a discrete (categorical) variable with two or more categories, using continuous and/or discrete predictors Addresses the same questions that discriminant analysis and multiple regression do but without distributional assumptions on the predictors the independent and dependent variables need not be linearly related Homoscedasticity is not necessary For a dichotomous response, you compute a single logit function; for a multi-level response, you create more than one logit function Why use Multinomial Logistic Regression? Multinomial Logistic regression is often used when the dependent variable is ordinal Then, cumulative logits are computed , which are based on the cumulative probabilities For three response levels (high, medium, low), let: q 1 = p 1 q 2 = p 1 + p 2 1 = p 1 + p 2 + p 3 And, you compute two cumulative logits: + = + = 3 2 1 2 3 2 1 1 ln ) logit( and ln ) logit( p p p q p p p q The log odds of high vs. medium or low The log odds of high or medium vs. low Multinomial Logistic Regression model Given a set of m predictor variables (categorical or continuous), the logit is: Thus, there are separate intercept parameters ( b 0 ) and different sets of regression parameters k ) for each logit m mk k k k X X b b b q + + + = ... ) logit( 1 1 0 Questions Can categories be correctly predicted given a set of predictors? Usually once this is established the predictors are manipulated to see if the equation can be simplified. Comparison of equation with predictors plus intercept to a model with just the intercept What is the strength of association between the outcome variable and a set of predictors?

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