An Introduction to Statistical Modelling

Preface.

1. Introduction.

1.1 Models in data analysis.

1.2 Populations and samples.

1.3 Variables and factors.

1.4 Observational and experimental data.

1.5 Statistical models.

2. Distributions and inference.

2.1 Random variables and probability distributions.

2.2 Probability distributions as models.

2.3 Some common distributions.

2.4 Sampling distributions.

2.5 Inference.

2.6 Postscript.

3. Normal response and quantitative explanatory variables: regression.

3.1 Motivation.

3.2 Simple regression.

3.3 Multiple regression.

3.4 Model building.

3.5 Model validation and criticism.

3.6 Comparison of regressions.

3.7 Non-linear models.

4. Normal response and qualitative explanatory variables: analysis of variance.

4.1 Motivation.

4.2 One-way arrangements.

4.3 Cross-classifications.

4.4 Nested classifications.

4.5 A general approach via multiple regression.

4.6 Analysis of covariance.

5. Non-normality: the theory of generalized linear models.

5.1 Introduction.

5.2 The generalized linear model.

5.3 Fitting the model.

5.4 Assessing the fit of a model: deviance.

5.5 Comparing models: analysis of deviance.

5.6 Normal models.

5.7 Inspecting and checking models.

5.8 Software.

6. Binomial response variables: logistic regression and related method.

6.1 Binary response data.

6.2 Modelling binary response probabilities.

6.3 Logistic regression.

6.4 Related methods.

6.5 Ordered polytomous data.

7. Tables of counts and log-linear models.

7.1 Introduction.

7.2 Data mechanisms and distributions.

7.3 Log-linear models for means.

7.4 Models for contingency tables.

7.5 Analysis.

7.6 Applications.

8. Further topics.

8.1 Introduction.

8.2 Continuous non-normal responses.

8.3 Quasi-likelihood.

8.4 Overdispersion.

8.5 Non-parametric models.

8.6 Conclusion: the art of model building.

References.

Index.