Rubric posted at the end of this document

1. [__/10] The first question is about moderated mediation question.

Assume that the DV distribution is appropriate for regression (unless you are asked to evaluate it). You do not have to test regression assumptions, except insofar as the questions below specifically ask you to. Evaluate and test the model that follows with lavaan. When bootstrapping, please use 1,000 bootstrapped samples.

Data are in Class14_homework_2022.csv. Investigators examined whether the influence of physical activity on quality of life was mediated by radical hope*. Their sample was further divided into two groups of non-demented adults aged 65 and older: (1) African American adults (n=100) or (2) Hispanic White adults (n=99). Participants were adults aged 20-39. Investigators were also interested in whether the direct and indirect relationships of physical activity on self-rated quality of life differed for the racial/ethnicity groups. For all constructs except race/ethnicity, higher scores mean the participant has more of the named trait. Note1: Race/Ethnicity is coded as 0=African American, 1=Hispanic White; do not center this variable or it will cause a problem for lavPredict. Note2: For plotting purposes, after youve created the lavPredict dataframe, you may want to convert Ethnicity to a character variable (e.g., -African American-, -Hispanic White-) and use this variable as the color/group variable in your ggplot2 moderation plots.

*Radical Hope is defined by the investigators as “1) Understanding the history of oppression along with the resistance and actions taken to transform these conditions, 2) envisioning more equitable possibilities, 3) embracing ancestral pride, 4) creating meaning and purpose in life by adopting a more socially just orientation.”

Run the model and try to interpret it. You can be fairly broad and global in your discussion, focusing on the mediation, whether there is evidence that either the a- or the c-path are moderated and (if yes) what the resulting conditional direct and indirect effects tell you. Plotting the two moderations (int1, int2) separately for Radical Hope and Quality of Life will aid in interpretation.

2. [__/10] The second question is about Bayesian regression. The same investigators wanted to use a Bayesian approach to test the multiple regression model “Quality of Life= Physical Activity+ (African American or White Hispanic) + Radical Hope”. Using Bayesian regression in jqs, obtain the results. Accept all defaults, including using uninformative uniform priors. Report and interpret the r-squared and the Bayes Factor for the entire regression. (i.e., global r-squared). Also, report and interpret the BFInclusion and the 95% Bayesian credible interval for each b-weight. PLEASE DO NOT use the words -significance-, or -confidence interval-, since neither exist in Bayesian regression. Bayes Factors tell us about the strength of support (or weakness of support) for a hypothesis.

Rubric

Q1

10-point 9-point 8-point 7-point 0-point

? Conducting a moderated mediation analysis in lavaan

o Please use 1,000 bootstrapped samples

? Providing the following output for the moderated mediation regression:

o parameterEstimates table (coefficient, se, bca.simple 95% confidence intervals) for the following paths and defined parameters:

- a-path (X to M)

- b-path (M to Y)

- c-path (X to Y)

- w1-path (main effect of moderator on M)

- w2-path (main effect of moderator on Y)

- ind1 (indirect effect of X on Y)

- int1 (X*moderator interaction eff on M)

- int2 (X*moderator interaction eff on M)

- conditional direct effects of the X variable on the Y outcome at different levels of the moderator

- conditional indirect effects of the X variable on the Y outcome at different levels of the moderator

- Moderator plot for the mediator as outcome

- Moderator plot for the Y-outcome

In your narrative, summarize

- The regression model predicting the mediator

- The regression model predicting the ultimate outcome.

- The overall indirect effect of X

- The indirect effect of X in each group, and whether that indirect effect differs significantly by moderator group

- The direct effect of X in each group, and whether that indirect effect differs significantly by moderator group

- global conclusion summarizing whether or not you have conditional indirect or direct effects, and more generally what these results mean. Missing one or two elements of a #10 answer. Commonly this means incomplete reporting of statistics, or incomplete narrative. May be substantially a “10” or “9” answer, but there is at least one computation or setup error that results in one or more incorrect numbers. All elements of the answer may be excellent, but the answer is “wrong” due to incorrect computations/calculations. Alternatively, an “8” could indicate an answer that is simply missing more elements than a “9” answer (e.g., 3+ elements), but the answer is correct enough to warrant higher than a “7”. “mercy point” (e.g., you really don’t deserve a point, but because you made some attempt, this is acknowledged; example: doing a “descriptives” when the question can only be fulfilled by a “frequencies”, dumping output but no interpretation) No response, or you put the wrong output [e.g., for the wrong question] in your answer. Evidence of minimal effort or attention.

Q2

10-point 9-point 8-point 7-point 0-point

? Conducting a Bayesian regression in jsq with the specified DV and IVs.

o Using default uniform priors

? Providing the following output for the Bayesian regression:

o Model Comparison table

o Posterior Summary table

In your narrative

(a) Summarize statistical evidence of whether the overall Bayes Factor and R2 results support the null hypothesis for the model, or the alternative hypothesis. Be sure to comment on the strength or weakness of the evidence.

(b) For each b-weight, summarize coefficient (direction), the BFInclusion, and whether the 95% Bayesian credible interval supports the null hypothesis or the alternative hypothesis regarding each predictor.

(c) global conclusion summarizing the regression (which predictors seem to have positive or negative effects on the outcome, and what it means)

Missing one or two elements of a #10 answer. Commonly this means incomplete reporting of statistics, or incomplete narrative. May be substantially a “10” or “9” answer, but there is at least one computation or setup error that results in one or more incorrect numbers. All elements of the answer may be excellent, but the answer is “wrong” due to incorrect computations/calculations. Alternatively, an “8” could indicate an answer that is simply missing more elements than a “9” answer (e.g., 3+ elements), but the answer is correct enough to warrant higher than a “7”. “mercy point” (e.g., you really don’t deserve a point, but because you made some attempt, this is acknowledged; example: doing a “descriptives” when the question can only be fulfilled by a “frequencies”, dumping output but no interpretation) No response, or you put the wrong output [e.g., for the wrong question] in your answer. Evidence of minimal effort or attention.

1. [__/10] The first question is about moderated mediation question.

Assume that the DV distribution is appropriate for regression (unless you are asked to evaluate it). You do not have to test regression assumptions, except insofar as the questions below specifically ask you to. Evaluate and test the model that follows with lavaan. When bootstrapping, please use 1,000 bootstrapped samples.

Data are in Class14_homework_2022.csv. Investigators examined whether the influence of physical activity on quality of life was mediated by radical hope*. Their sample was further divided into two groups of non-demented adults aged 65 and older: (1) African American adults (n=100) or (2) Hispanic White adults (n=99). Participants were adults aged 20-39. Investigators were also interested in whether the direct and indirect relationships of physical activity on self-rated quality of life differed for the racial/ethnicity groups. For all constructs except race/ethnicity, higher scores mean the participant has more of the named trait. Note1: Race/Ethnicity is coded as 0=African American, 1=Hispanic White; do not center this variable or it will cause a problem for lavPredict. Note2: For plotting purposes, after youve created the lavPredict dataframe, you may want to convert Ethnicity to a character variable (e.g., -African American-, -Hispanic White-) and use this variable as the color/group variable in your ggplot2 moderation plots.

*Radical Hope is defined by the investigators as “1) Understanding the history of oppression along with the resistance and actions taken to transform these conditions, 2) envisioning more equitable possibilities, 3) embracing ancestral pride, 4) creating meaning and purpose in life by adopting a more socially just orientation.”

Run the model and try to interpret it. You can be fairly broad and global in your discussion, focusing on the mediation, whether there is evidence that either the a- or the c-path are moderated and (if yes) what the resulting conditional direct and indirect effects tell you. Plotting the two moderations (int1, int2) separately for Radical Hope and Quality of Life will aid in interpretation.

2. [__/10] The second question is about Bayesian regression. The same investigators wanted to use a Bayesian approach to test the multiple regression model “Quality of Life= Physical Activity+ (African American or White Hispanic) + Radical Hope”. Using Bayesian regression in jqs, obtain the results. Accept all defaults, including using uninformative uniform priors. Report and interpret the r-squared and the Bayes Factor for the entire regression. (i.e., global r-squared). Also, report and interpret the BFInclusion and the 95% Bayesian credible interval for each b-weight. PLEASE DO NOT use the words -significance-, or -confidence interval-, since neither exist in Bayesian regression. Bayes Factors tell us about the strength of support (or weakness of support) for a hypothesis.

Rubric

Q1

10-point 9-point 8-point 7-point 0-point

? Conducting a moderated mediation analysis in lavaan

o Please use 1,000 bootstrapped samples

? Providing the following output for the moderated mediation regression:

o parameterEstimates table (coefficient, se, bca.simple 95% confidence intervals) for the following paths and defined parameters:

- a-path (X to M)

- b-path (M to Y)

- c-path (X to Y)

- w1-path (main effect of moderator on M)

- w2-path (main effect of moderator on Y)

- ind1 (indirect effect of X on Y)

- int1 (X*moderator interaction eff on M)

- int2 (X*moderator interaction eff on M)

- conditional direct effects of the X variable on the Y outcome at different levels of the moderator

- conditional indirect effects of the X variable on the Y outcome at different levels of the moderator

- Moderator plot for the mediator as outcome

- Moderator plot for the Y-outcome

In your narrative, summarize

- The regression model predicting the mediator

- The regression model predicting the ultimate outcome.

- The overall indirect effect of X

- The indirect effect of X in each group, and whether that indirect effect differs significantly by moderator group

- The direct effect of X in each group, and whether that indirect effect differs significantly by moderator group

- global conclusion summarizing whether or not you have conditional indirect or direct effects, and more generally what these results mean. Missing one or two elements of a #10 answer. Commonly this means incomplete reporting of statistics, or incomplete narrative. May be substantially a “10” or “9” answer, but there is at least one computation or setup error that results in one or more incorrect numbers. All elements of the answer may be excellent, but the answer is “wrong” due to incorrect computations/calculations. Alternatively, an “8” could indicate an answer that is simply missing more elements than a “9” answer (e.g., 3+ elements), but the answer is correct enough to warrant higher than a “7”. “mercy point” (e.g., you really don’t deserve a point, but because you made some attempt, this is acknowledged; example: doing a “descriptives” when the question can only be fulfilled by a “frequencies”, dumping output but no interpretation) No response, or you put the wrong output [e.g., for the wrong question] in your answer. Evidence of minimal effort or attention.

Q2

10-point 9-point 8-point 7-point 0-point

? Conducting a Bayesian regression in jsq with the specified DV and IVs.

o Using default uniform priors

? Providing the following output for the Bayesian regression:

o Model Comparison table

o Posterior Summary table

In your narrative

(a) Summarize statistical evidence of whether the overall Bayes Factor and R2 results support the null hypothesis for the model, or the alternative hypothesis. Be sure to comment on the strength or weakness of the evidence.

(b) For each b-weight, summarize coefficient (direction), the BFInclusion, and whether the 95% Bayesian credible interval supports the null hypothesis or the alternative hypothesis regarding each predictor.

(c) global conclusion summarizing the regression (which predictors seem to have positive or negative effects on the outcome, and what it means)

Missing one or two elements of a #10 answer. Commonly this means incomplete reporting of statistics, or incomplete narrative. May be substantially a “10” or “9” answer, but there is at least one computation or setup error that results in one or more incorrect numbers. All elements of the answer may be excellent, but the answer is “wrong” due to incorrect computations/calculations. Alternatively, an “8” could indicate an answer that is simply missing more elements than a “9” answer (e.g., 3+ elements), but the answer is correct enough to warrant higher than a “7”. “mercy point” (e.g., you really don’t deserve a point, but because you made some attempt, this is acknowledged; example: doing a “descriptives” when the question can only be fulfilled by a “frequencies”, dumping output but no interpretation) No response, or you put the wrong output [e.g., for the wrong question] in your answer. Evidence of minimal effort or attention.

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