Illustrating DyadR Using the Truth & Bias Model

David A. Kenny

March 11, 2015

Powerpointdavidakenny.net/DyadR/DyadR.ppt

Datadavidakenny.net/DyadR/Acitelli_Individual.savdavidakenny.net/DyadR/Acitelli_Dyad.savdavidakenny.net/DyadR/Acitelli_Pairwise.sav

Outputdavidakenny.net/DyadR/DyadR_Output.pdf

Overview•Truth and Bias (T&B) Model• Illustration from Acitelli Dataset

•Use DyadR Programs to Estimate and Test a T&B Model

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The Truth and Bias Model (T&B)

West, T. V., & Kenny, D. A. The truth and bias model of judgment (T&B). Psychological Review, 118, 357–378.

Basic Idea of the T&B Model

• Theoretical and empirical framework designed to address the basic questions of how accuracy and bias operate, and the nature of their interdependence

• Judgment is determined by the truth (T) and bias (B).

• Accuracy is defined as a relationship not an event.

Types of Bias in the T&B Model

• Some biases are measured using variables– For the bias of assumed similarity, bias is

measured using the perceivers’ self-judgment.– For the bias of perseveration, bias is

measured as prior judgment.

Directional Bias• How strongly judgments are pulled

away from the mean level of the truth• The extent to which perceivers’ under-

or-overestimate the average value of the truth

• With proper scaling can be obtained from the intercept in the regression equation.

Moderators• Variables that inform how the processes of

accuracy and bias occur by influencing the strength of the forces

• Can moderate the truth force, the bias force, directional bias, or all three

• A moderator may have one effect on the truth force and another effect on the bias force.

Key Measurement Issue

Measure Truth, Bias Variables, and Judgment using the same scale.

Center Truth, Bias Variables and Judgment using the truth mean.

Directional bias becomes the regression intercept in the model.

Acitelli Study

• Sample 148 married and 90 dating couples in the Detroit area

• Outcome – Your partner’s relationship with the child

(children) is good (1 to 5). • Predictor Variable

– Your relationship with the child (children) is good (1 to 5).

• Covariate: Married (1)vs. dating (-1)9

Woman’s Perception of Man’s Rel.

with Child

T&B Example

Man’s Perception of Woman’s Rel.

with Child

Female Bias

Male Bias

Male Accuracy

Female

Accuracy

Because the data are dyadic, there are two accuracy and bias effects.

We can estimate the above model using the Actor-Partner Interdependence Model (Kashy & Kenny).

Woman’s Rel. with Child

Man’s Rel. with Child

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What We Need To Do

• Restructure Data

• Examine Distinguishability

• Estimate the APIM

We shall use DyadR.

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What is DyadR?• Package of programs written in R for dyadic

analysis.– R is open source– free

• DyadR is written as a “shiny” app and no knowledge of R is needed.

• Provides not only the usual computer output, but also text, tables, suggestions, and figures.• Done in collaboration with others (Tom

Ledermann at Utah State, Lara Stas at Ghent, and Rob Ackerman at Texas Dallas)

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Task 1: Restructure Data

• Ordinarily dyad data are entered by individual: one record person.

• Analysis requires other formats:– Dyad – Pairwise

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Individual Data Structure

Individual

Dyad Person X Y Z

1 1 5 9 3

1 2 2 8 3

2 1 6 3 7

2 2 4 6 7

3 1 3 6 5

3 2 9 7 5

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Dyad Data Structure

 

Dyad X1 Y1 X2 Y2 Z

1 5 9 2 8 3

2 6 3 4 6 7

3 3 6 9 7 5

 

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Subscripts 1 and 2 refer to roles like man and woman.

Pairwise Data Structure 

Dyad Person X1 Y1 X2 Y2 Z

1 1 5 9 2 8 3

1 2 2 8 5 9 3

2 1 6 3 4 6 7

2 2 4 6 6 3 7

3 1 3 6 9 7 5

3 2 9 7 3 6 5

Subscripts 1 and 2 refer to respondent and partner.

Apps• Individual to Dyad: ItoD

– https://davidakenny.shinyapps.io/ItoD/

• Individual to Pairwise: ItoP– https://davidakenny.shinyapps.io/ItoP/

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ItoD: Text“The dataset has been transformed from an individual to a dyad dataset called OutputData. The distinguishing variable is Gender_num, and it has two levels, Women (-1) and Men (1). There are 238 dyads and 476 individuals, 238 Women and 238 Men. There are missing data for one or more of the variables in the dataset. The listwise deleted dataset contains 145 dyads and 278 individuals. There are 4 variables, 1 between-dyad variable, 1 within-dyad variable, and 2 mixed variables. There is one variable that is a string or character variable which has been deleted from the dataset and it is Gender. The one between-dyad variable is Married, and the one within-dyad variable is Gender Numeric. The within-dyads variable, Gender Numeric, is a dichotomy and could be used as a distinguishing variable.”

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ItoD: First Table

Mean sd Minimum Maximum Intraclass r N

Gender Numeric 0.000 1.001 -1.000 1.000 -1.000 476

Married 0.244 0.971 -1.000 1.000 1.000 476

Close to Child 0.000 0.487 -1.767 0.233 0.207 279

Partner Close to Child -0.066 0.583 -2.767 0.233 0.133 278

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The descriptive statistics for the variables as individuals are below. Sample sizes are given in the last column of the table for each variable.

ItoD: Second Table

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Mean sd

Women Men p Women Men p r p N

Close to Child 0.017 -0.028 .398 0.481 0.505 .567 .230 .007 134

Partner Close to Child -0.135 0.015 .023 0.645 0.482 <.001 .129 .137 133

The descriptive and inferential statistics for the mixed andwithin-dyads variables as dyads are below. Sample sizes are given in the last column in both tables. For table below, the number of cases refers to the number with complete data for both members. Degrees of freedom for the test of mean difference are one less the sample size and for the test of standard deviation difference and the test of the correlation are two less the sample size.

Task 2: Determine whether dyad members are

distinguishable.• Each dyad consists of a man and woman.

• Can we ignore gender? If so, dyad members are said to be “indistinguishable.”

• By doing so, we obtain a simpler model with more power to test hypotheses.

• https://davidakenny.shinyapps.io/Dingy/

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Results from Dingy

• Conclusion: “Because all of the models have poor fit (both in terms of the chi-square test and the RMSEA), and because the SABIC is lowest for the model of complete distinguishability (see Table 2), it seems reasonable to assume that dyad members are fully distinguishable.”

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chi square df p value

Means 8.138 2 .017

Correlations 8.535 4 .074

Variances 15.178 2 <.001

Table 3: Tests of Hypotheses of Different Types of Distinguishability

Task 3: Use the APIM to Estimate and Test T&B, Treating Dyad Members as Distinguishable

• Pairwise Dataset

• Perceptions of Partner’s Closeness to the Child is predicted by Actual Closeness and Own Closeness, an APIM.

• https://davidakenny.shinyapps.io/APIM_MM/

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Suggestions from APIM_MM

1. There is one outlier (standardized residual greater than 4.0 or less than 4.0) for P Close to Child. Examine the output to see what observation might be considered to be an outlier.

2. There is evidence of negative skew in the residuals of P Close to Child.

(many other suggestions are possible)

T&B Results: Truth and Bias Results

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Differences by Gender?• “The test that the two actor effects are statistically

significantly different is not significant, Z = -1.913 (p = .057).”

• “The test that the two partner effects are statistically significantly different is not significant, Z = -0.989 (p = .324).”

• “The combined actor effect across both Women and Men is equal to 0.541 and is statistically significant (p < .001) and the standardized effect equals 0.463 (r = .448 and a medium effect size). The combined partner effect across both Women and Men is equal to 0.134 and is statistically significant (p = .033) and the standardized effect equals 0.115 (r = .143 and a small effect size).” 40

T&B: Directional Bias?

• Women: -0.213, p < .001• Men: -0.049, p = .300• Overall: -0.131, p = .017• Gender Difference: p = .008• Moderation by Marital Status: 0.097, p =

.027• Married: -0.034• Dating: -0.228 41

Future Work• APIM Options

• Moderators• Non-normal outcomes• Remove outliers• Mediation models• SEM estimation

• Alternative dyadic models• Common fate & mutual influence

• Alternative dyadic designs• SRM and One-with-Many designs

• Longitudinal dyadic models 42

Thank You!Powerpoint

davidakenny.net/DyadR/DyadR.ppt

Data

davidakenny.net/DyadR/Acitelli_Individual.sav

davidakenny.net/DyadR/Acitelli_Dyad.sav

davidakenny.net/DyadR/Acitelli_Pairwise.sav

Output

http://davidakenny.net/DyadR/DyadR_Output.pdf

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