follow the three r’s: respect for self, respect for others
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Follow the three R’s: Respect for self, Respect for others and Responsibility for all your actions. Categorical Data Analysis. Chapter 1: Introduction Chapter 2: Two Way Tables. The Role of a Variable. Explanatory/predictor/independent variable Response/outcome/dependent variable - PowerPoint PPT PresentationTRANSCRIPT
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Follow the three R’s: Respect for self,
Respect for others and Responsibility for all your actions
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Categorical Categorical Data AnalysisData Analysis
Chapter 1: IntroductionChapter 1: IntroductionChapter 2: Two Way TablesChapter 2: Two Way Tables
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A variable
Categorical/Qualitative
Numerical/Quantitative
Nominal variable Ordinal variable Discrete variable Continuous variable
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The Role of a VariableThe Role of a Variable• Explanatory/predictor/independent
variable
• Response/outcome/dependent variable
Q: Will women smoking during pregnancy have higher probability of miscarriage?
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Statistical Tools vs. Variable TypesStatistical Tools vs. Variable Types
Response (output)
Explanatory var (input)Numerical Categorical/Mixed
Numerical•Simple and Multiple Regression
•Analysis of Variance (ANOVA)•Analysis of Covariance (ANCOVA)
Categorical Categorical data analysis
Distributions for Categorical DataDistributions for Categorical Data
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• Binomial data• When the sample size n is fixed and the response per subject is binary
• Multinomial data• When the sample size n is fixed and the response per subject is multinary
• Poisson data• When the sample size n is not fixed and the response per subject is binary/multinary
• Poisson model conditional on a given n is Binomial/ Multinomial model (Sec. 1.2.5)
Distributions for Categorical DataDistributions for Categorical Data• These models have overdispersion
problem because they assume all subjects having the same probability of responding (from the same population) and ignore the covariates
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Review: Maximum Likelihood Review: Maximum Likelihood Inference MethodInference Method
• Likelihood functions• MLE (maximum likelihood estimate)• Asymptotical distribution of mle• Wald inference (test and confidence
interval)• Example: binomial data
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Two-Way TablesTwo-Way Tables• A table summarizes two categorical
variables• Cells of a two-way table are
frequency counts of combined outcomes of the two variables
• Called IxJ tables for I rows and J columns
Eg. Do you believe “afterlife”?
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Probability & IndependenceProbability & Independence• Joint probability• Marginal probability• Conditional probability
– Sensitivity = P(+ | disease)– Specificity = P( - | no disease)
• Independence of X and Y
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Three Sampling MethodsThree Sampling Methods• Poisson sampling: no fixed total
• Single multinomial sampling: fixed grand total
• Independent multinomial sampling: fixed row or column totals
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Comparing Proportions in Comparing Proportions in 2x2 Tables2x2 Tables
• Difference of proportions: pi1-pi2
• Relative risk: pi1/pi2
• Odds Ratio: odds1/odds2odds1=pi1/(1-pi1)odds2=pi2/(1-pi2)
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More on Odds RatioMore on Odds Ratio• Properties
• Inference
• Relationship to relative risk
Comparing Proportions in Comparing Proportions in stratified 2x2 Tablesstratified 2x2 Tables
• Find the “conditional odds rations” describing the partial association in stratified 2x2 tables
• Marginal vs. conditional independence
• Homogeneous association• Same idea applying to IxJ tables
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Table 2.7Table 2.7Response
Clinic Treatment Success Failure
1 A 18 12
B 12 8
2 A 2 8
B 8 32
Total A 20 20
B 20 40
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