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664What is the Exponential Family of Distributions?
665Canonical Form of Exponential Family Distributions
666Natural Parameter and Sufficient Statistics
667Mean and Variance in the Exponential Family
668Common Distributions as Exponential Family Members
669The Dispersion Parameter φ
670Why Exponential Family Matters for GLMs
671What is a Link Function?
672The Identity Link
673The Logit Link
674The Probit Link
675The Log Link
676Canonical vs Non-Canonical Links
677Interpreting Coefficients Under Different Links
678Choosing the Right Link Function
679Logistic Regression Setup and the Binary Response
680The Logit Link Function and Odds
681Interpreting Logistic Regression Coefficients
682Maximum Likelihood Estimation in Logistic Regression
683Hypothesis Tests for Individual Coefficients
684Likelihood Ratio Tests for Model Comparison
685Confidence Intervals for Odds Ratios
686Assumptions and Diagnostics in Logistic Regression
687Categorical Predictors and Interactions in Logistic Models
688Effect Size and Practical Significance
689When to Use Poisson Regression
690The Poisson Distribution as a GLM
691Interpreting Poisson Coefficients
692Offset Terms for Exposure
693Overdispersion in Count Data
694Quasi-Poisson and Negative Binomial Models
695Zero-Inflated Models
696Poisson Regression Applications
697Deviance: A Measure of Model Fit
698Null and Residual Deviance
699The Likelihood Ratio Test
700AIC and BIC for Model Selection
701Deviance Residuals
702Pseudo R-Squared Measures
703Sequential Model Building Strategy

664What is the Exponential Family of Distributions?
665Canonical Form of Exponential Family Distributions
666Natural Parameter and Sufficient Statistics
667Mean and Variance in the Exponential Family
668Common Distributions as Exponential Family Members
669The Dispersion Parameter φ
670Why Exponential Family Matters for GLMs
671What is a Link Function?
672The Identity Link
673The Logit Link
674The Probit Link
675The Log Link
676Canonical vs Non-Canonical Links
677Interpreting Coefficients Under Different Links
678Choosing the Right Link Function
679Logistic Regression Setup and the Binary Response
680The Logit Link Function and Odds
681Interpreting Logistic Regression Coefficients
682Maximum Likelihood Estimation in Logistic Regression
683Hypothesis Tests for Individual Coefficients
684Likelihood Ratio Tests for Model Comparison
685Confidence Intervals for Odds Ratios
686Assumptions and Diagnostics in Logistic Regression
687Categorical Predictors and Interactions in Logistic Models
688Effect Size and Practical Significance
689When to Use Poisson Regression
690The Poisson Distribution as a GLM
691Interpreting Poisson Coefficients
692Offset Terms for Exposure
693Overdispersion in Count Data
694Quasi-Poisson and Negative Binomial Models
695Zero-Inflated Models
696Poisson Regression Applications
697Deviance: A Measure of Model Fit
698Null and Residual Deviance
699The Likelihood Ratio Test
700AIC and BIC for Model Selection
701Deviance Residuals
702Pseudo R-Squared Measures
703Sequential Model Building Strategy

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Lesson 667 of 2,145·18. Generalized Linear ModelsPro lesson

Mean and Variance in the Exponential Family

How E(Y) = b'(θ) and Var(Y) = b''(θ)a(φ), deriving mean and variance from the cumulant function.

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