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CLG Topic 13 - Topic 13 Handout Random Effects Learning...

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Topic 13 Handout: Random Effects Learning Goals: (1) Understand the differences between fixed effects and random effects models; (2) Be able to identify effects as either fixed or random; (3) Be able to utilize EMS (expected mean squares) to determine (a) appropriate tests and (b) estimates for variances; (4) Be able to interpret and draw appropriate conclusions from ANOVA models where random effects are involved. 13.1 Three scenarios are given below. For each of these, suggest at least one research question of interest. Then identify the response variable and all factors involved in the study. As you identify factors, determine the number of levels for each factor and whether each factor should be treated as a fixed or random effect. a. Auto manufacturer wants to study the effects of differences between drivers (A) and differences between cars (B) on gasoline consumption. Four drivers were selected at random, and additionally five cars of the same model with manual transmissions were randomly taken from the assembly line. Each driver drove each car twice over a 40-mile test course and the MPG were recorded. b. A researcher studied the sodium content of six brands of U.S. beers sold in a metropolitan area. For each beer, both the regular and light versions were examined. c. Twelve job applicants were rated by each of the three personnel officers for a company. Each applicant was rated by each officer. We want to explore whether there are differences among the personnel officers. Scenario I : (From KNNL Applied Linear Statistical Models ) An automobile manufacturer wishes to study the difference between drivers (factor A, 4 levels) and between cars (factor B, 5 levels) on gasoline consumption. The data are given in the associated SAS file. NOTE: This scenario will simply be used for an in-class example. All output has been provided below on pages 1-3. You may wish to refer to it as we talk about the example in class. To treat effects as random, a “random” statement is required in the GLM coding: proc glm ; class driver car; model gas=driver|car; random driver car driver*car / test ; run ; Note that the random statement must include interactions that are random as well. The code above creates the following output (somewhat edited for convenience):
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Page 2 Dependent Variable: gas Sum of Source DF Squares Mean Square F Value Pr > F Model 19 377.4447500 19.8655132 113.03 <.0001 Error 20 3.5150000 0.1757500 Corrected Total 39 380.9597500 R-Square Coeff Var Root MSE gas Mean 0.990773 1.395209 0.419225 30.04750 Source DF Type I SS Mean Square F Value Pr > F driver 3 280.2847500 93.4282500 531.60 <.0001 car 4 94.7135000 23.6783750 134.73 <.0001 driver*car 12 2.4465000 0.2038750 1.16 0.3715 Source DF Type III SS Mean Square F Value Pr > F driver 3 280.2847500 93.4282500 531.60 <.0001 car 4 94.7135000 23.6783750 134.73 <.0001 driver*car 12 2.4465000 0.2038750 1.16 0.3715 Source Type III Expected Mean Square driver Var(Error) + 2 Var(driver*car) + 10 Var(driver) car Var(Error) + 2 Var(driver*car) + 8 Var(car) driver*car Var(Error) + 2 Var(driver*car) Tests of Hypotheses for Random Model Analysis of Variance Dependent Variable: gas Source DF Type III SS Mean Square F Value Pr > F driver 3 280.284750 93.428250 458.26 <.0001 car 4 94.713500 23.678375 116.14 <.0001 Error 12 2.446500 0.203875 Error: MS(driver*car) Source DF Type III SS Mean Square F Value Pr > F driver*car 12 2.446500 0.203875 1.16 0.3715
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