In analysis of variance, if the levels of some factors are associated with quantitative values, these values can be used in the analysis. For example, in a balanced two-factor ANOVA where factors are two kinds of fertilizer and levels are different quantitative amounts of fertilizers, an ANOVA would often examine linear and higher-order contrasts in the main effects and polynomial contrasts in the interaction (e.g., the linear-by-linear contrast). This chapter explores similar ideas for log-linear models. Much of Christensen (Analysis of variance, design, and regression: Linear modeling for unbalanced data, (2nd edn.). Chapman and Hall, 2015) is devoted to exploring such methods for unbalanced ANOVA models and its Chapters 20 and 21 specifically extend those ideas to logistic regression and log-linear models. This chapter was the progenitor of those applications.

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Models for Factors with Quantitative Levels

  • Ronald Christensen

摘要

In analysis of variance, if the levels of some factors are associated with quantitative values, these values can be used in the analysis. For example, in a balanced two-factor ANOVA where factors are two kinds of fertilizer and levels are different quantitative amounts of fertilizers, an ANOVA would often examine linear and higher-order contrasts in the main effects and polynomial contrasts in the interaction (e.g., the linear-by-linear contrast). This chapter explores similar ideas for log-linear models. Much of Christensen (Analysis of variance, design, and regression: Linear modeling for unbalanced data, (2nd edn.). Chapman and Hall, 2015) is devoted to exploring such methods for unbalanced ANOVA models and its Chapters 20 and 21 specifically extend those ideas to logistic regression and log-linear models. This chapter was the progenitor of those applications.