Model Comparison Approach To Regression Anova And Beyond Third Edition

The model comparison approach to regression ANOVA is a powerful and flexible method for analyzing data from experiments. It is based on the idea of comparing different models to each other in order to determine which model best fits the data. This approach can be used to test hypotheses about the effects of different independent variables on a dependent variable, and to make predictions about the dependent variable based on the values of the independent variables.

Data Analysis: A Model Comparison Approach To Regression, ANOVA, and Beyond, Third Edition

by Charles M. Judd

4.3 out of 5

Language	:	English
File size	:	6453 KB
Screen Reader	:	Supported
Print length	:	378 pages

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The model comparison approach is a departure from the traditional ANOVA approach, which focuses on testing the significance of individual effects. In the model comparison approach, the focus is on finding the model that best fits the data, regardless of whether the effects are statistically significant. This approach can lead to a more accurate and informative understanding of the data.

Model Selection

The first step in the model comparison approach is to select a set of models to compare. The models should be based on the research question and the data that is available. The models should also be nested within each other, meaning that each model includes all of the terms from the previous model, plus one additional term.

For example, if the research question is to determine the effect of advertising expenditure on sales, the following models could be used:

• Model 1: Sales = b0 + e
• Model 2: Sales = b0 + b1 * Advertising + e
• Model 3: Sales = b0 + b1 * Advertising + b2 * Advertising^2 + e

Model 1 is the simplest model, and it only includes an intercept term. Model 2 adds a term for advertising expenditure, and Model 3 adds a term for the squared value of advertising expenditure. The models are nested within each other, because Model 2 includes all of the terms from Model 1, and Model 3 includes all of the terms from Model 2.

Model Fitting

Once the models have been selected, they need to be fitted to the data. This involves estimating the values of the parameters in each model. The parameters are estimated using least squares, which minimizes the sum of the squared residuals. The residuals are the differences between the observed values of the dependent variable and the predicted values from the model.

Model Comparison

Once the models have been fitted, they need to be compared to each other to determine which model best fits the data. The models can be compared using a variety of criteria, including:

• R-squared: The R-squared value measures the proportion of variation in the dependent variable that is explained by the model. The higher the R-squared value, the better the model fits the data.
• Adjusted R-squared: The adjusted R-squared value is a variation of the R-squared value that takes into account the number of parameters in the model. The adjusted R-squared value is more conservative than the R-squared value, and it is often used to compare models with different numbers of parameters.
• AIC: The Akaike Information Criterion (AIC) is a measure of the goodness of fit of a model that takes into account the number of parameters in the model. The lower the AIC value, the better the model fits the data.

The best model is the model that has the highest R-squared value, the highest adjusted R-squared value, and the lowest AIC value. However, it is important to note that the best model is not necessarily the most complex model. The most complex model may overfit the data, which means that it captures the noise in the data as well as the signal. The best model is the model that provides the most accurate and informative description of the data.

Beyond ANOVA

The model comparison approach can be used to analyze data from any type of experiment, not just ANOVA experiments. The approach can be used to analyze data from regression experiments, ANCOVA experiments, and MANOVA experiments. The approach can also be used to analyze data from non-experimental studies, such as observational studies.

The model comparison approach is a powerful and flexible method for analyzing data. The approach can be used to test hypotheses about the effects of independent variables on a dependent variable, and to make predictions about the dependent variable based on the values of the independent variables. The approach can also be used to analyze data from experiments and from non-experimental studies.

References

• Belsley, D. A., Kuh, E., & Welsch, R. E. (1980). Regression diagnostics: Identifying influential data and sources of collinearity. New York: Wiley.
• Draper, N. R., & Smith, H. (1998). Applied regression analysis (3rd ed.). New York: Wiley.
• Fox, J. (2008). Applied regression analysis and generalized linear models (2nd ed.). Thousand Oaks, CA: Sage.
• Kutner, M. H., Nachtsheim, C. J., Neter, J., & Li, W. (2005). Applied linear regression models (5th ed.). New York: McGraw-Hill.

Data Analysis: A Model Comparison Approach To Regression, ANOVA, and Beyond, Third Edition

by Charles M. Judd

4.3 out of 5

Language	:	English
File size	:	6453 KB
Screen Reader	:	Supported
Print length	:	378 pages

FREE