Analysis of Regression Models and Interactions in Various Statistical Contexts

Page 1 of 4

Analysis of Regression Models and Interactions in Various Statistical Contexts - Page 1 preview image

Analysis of Regression Models and Interactions in Various Statistical Contexts5.24Expert testimony in homicide trials of battered women.Refer to the Duke Journal ofGender Law and Policy (Summer 2003) study of the impact of expert testimony on theoutcome of homicide trials involving battered woman syndrome, Exercise 5.3 (264).Recall that multipleregression was employed to model the likelihood of changing averdict from not guilty to guilty after deliberations, y, as function of juror gender (male orfemale) and expert testimony given (yes or no).a.Write a main efforts model for E(y) as a function of gender and expert testimony.Interpret the β coefficients in the model.The main efforts model for E(y) as a function of gender and expert testimony is()0112233E yxxx=+++Interpretation of model parameters011121231321which is mean of the combination of base levels, for any level B (1, 2), for any level B (1, 2), for any level F (1, 2,3)jjjjjjiiijji==−==−==−=Interaction Model with two qualitative independent variables, first one at threelevels F1,F2,F3 and second one at two levels B1,B2Then the equation is()01122334135231122334135231123The main effect term of F is&main effect term of B is,interaction term is,Dummy variables of x ,,are defined in the same way asEyxxxx xx xxxxx xx xxx and x=++++++for the main effects model.Now interpretation of model parameters

Page 2 of 4

Analysis of Regression Models and Interactions in Various Statistical Contexts - Page 2 preview image

Page 3 of 4

Analysis of Regression Models and Interactions in Various Statistical Contexts - Page 3 preview image

()()()()011121231321422122111532123111which is mean of the combination of base levels, for any level B (1, 2), for any level B (1, 2), for any level F (1, 2,3)jjjjjjiiijji==−==−==−==−−−=−−−The study or the impact of expert testimony on the outcome of homicide trials involvingbattered woman syndrome.The multipleregressionswas applied formodelingthe likelihood or changing a verdictfrom not guilty to guiltyafterdeliberations (y) as a function ofjurorgender male orfemale and expert testimony given.Now writing the main effects for model for E(y) as a function of gender and experttestimony and interpreting thecoefficients in this model.The main effects model is()01122E yxx=++Where111222is the main effect ofandis the main effect ofxxxxLet()11221();0;1 ifhas the value'yes'xif x is femaleotherwise xx==Now interpreting thecoefficients of the model011121231which is mean of the combination of base levels, for any level B (1, 2), for any level B (1, 2)jjjjjjjj==−==−=The interpretations of11(1, 2) is that there are two values forwhich is male and femalejxjx=And22(1, 2) is that there are two values forwhich is 'yes' or 'no'jxjx=b) Write an interaction model for E(y) as afunction of gender and expert testimony. Interpret theβ coefficients in the model.Now write an interaction effects model for E(y) as a function of gender and experttestimony and interpreting thecoefficients in the model.The main effect model is()01122312E yxxx x=+++ +Here12x xdenoted an interaction effects shown below.

Page 4 of 4

Analysis of Regression Models and Interactions in Various Statistical Contexts - Page 4 preview image

121212121)""""2)""""3)""""4)""""xFemale and xyesxmale and xyesxFemale and xnoxmale and xno========Now interested in interpreting thecoefficients in an interaction model.()()0010203000122whereis average effect when'' and''is the average effect when the variable characterstic is''FYFYyxmalexnoxyes==−=−=−−−===C) Based on datacollected on individual juror votes from past trials, the article reported that“when expert testimony was present, women jurors were more likely than men to change averdict from not guilty to guilty after deliberations.” Assume that when no expert testimony waspresent, male jurors were more likely than women to change a verdict from not guilty to guiltyafter deliberations. Which model, part a or part b, hypothesizes the relationships reported in thearticle? Illustrate the model with a sketchConsider the data collected on individual juror votes from the past trails. The reportwas when the expert testimony presents, the women jurors were more likely than men tochange a verdict from not guilty to guilty after deliberations.We are interested in determining the model part (a) or part (b) hypothesizes therelationship reported in this problem.The value of3is to be >0 , because21x=. We have the women jurors were morelikely than men to change averdict from not guilty toguilty after deliberations and when20x=the men jurors were more likely to change the verdict.In this case,0y, which the likelihood probability . since00We know that the women jurors are more likely to change their verdict from notguilty to guilty when the expert testimony was present.That is when12andis onexxthe expected probability or the likelihood ratio forthiseventisgreaterthantheexpectedprobabilityorthelikelihoodrationwhen12=0 and=1xxAlso men jurors are more likely to change their verdict from non-guilty to guiltywhen the expert testimony was absent.

Preview Mode

This document has 13 pages. Sign in to access the full document!

Report

Learning Tools

Writing Tools

Browse Resources

Analysis of Regression Models and Interactions in Various Statistical Contexts - Page 1

Study Now!

Document Details

Related Documents

Statistics - Univariate Inferential Tests

Statistics - Sampling

Statistics - Probability

Statistics - Principles of Testing

Statistics - Numerical Measures

Statistics - Introduction to Statistics

Statistics - Graphic Displays

Statistics - Cummulative Reviews

Statistics - Common Mistakes and Tables

Statistics - Bivariate Relationships

Company

Explore

Study Tools