PART I: Mediator Analysis
Leerkes and Crockenberg (1999) studied the relationship between how a new mother was raised by her own mother 20+ years before (maternal care - maternal) and the new mother's level of self-efficacy (efficacy) as a mother - the idea being that if your mother showed high levels of maternal care toward you; you in turn would feel more confident of your ability to mother your own child. But Leerkes and Crockenberg expected that this relation was mediated by self-esteem (esteem), such that if you had good maternal care, you will have good self-esteem, and if you have good self-esteem, that will, in turn, lead you to have higher self-efficacy. You will find the data in the dataset Maternal Care.
Test whether self-esteem mediates the effect between maternal care and self-efficacy. Your answer should include the following parts:
1. Construct(draw) a path diagram showing the mediating relation between the three variables of interest.
2. Use the following testing framework outlined in the Baron & Kenny (1986) article. Conduct a sequence of regression analysis to confirm each condition:
Condition 1: The independent variable must affect the mediator.
Condition 2: The independent variable must affect the dependent variable.
Condition 3: The mediator must affect the dependent variable when the dependent variable is regressed on the mediator and independent variable together.
Please use the statistical write-up. Make a conclusion about whether there is a mediating relation.
3. Using the unstandardized regression coefficients, demonstrate that the indirect effect is equal to the difference in regression coefficients of maternal care on self-efficacy. That is in Baron & Kenny language - does a*b = c-c'?
4. Conduct a hypothesis test to see if the indirect effect is significantly different from zero using the z-test. Show how you calculate standard error for the indirect effect.
5. Conduct a hypothesis test to see if the indirect effect is significantly different from zero using the empirical M-test. (Hint: You may want to use a web application)
6. Discuss benefits and limitations of three different approaches that you conducted above to answer Questions 2, 4, and 5.
PART II: Missing Data Analysis
In a computer program of your choice, open the Crime-m.csv (or Crime-m.sav) data set. Suppose you want to predict crime rate (crime) based on percentage living in a metropolitan area (pctmetro), percentage that are white (pctwhite), percentage living in poverty (poverty), and percentage of single parent families (single).
1. Report the percentages of missing values for each variable and discuss the results briefly.
2. Generate missing value indicators (a dummy coded variable for each predictor) and conduct a proper analysis to see if the missing pattern is associated with crime levels. Comment on the what you found out of the analysis.
3. Conduct the following set of analyses and report the results (e.g., regression coefficients, standard errors, R2, F-ratio, p-values, etc) in an APA-formatted table Briefly discuss similarities and differences in the results when missing values are treated differently.
a) Regress crime rate on four predictors that are mentioned above. For this analysis, use the list wise deletion to deal with missing values.
b) Run the same multiple regression model after substituting missing values with the mean of each variable.
c) Run the same multiple regression model using multiple imputation (M=5) to deal with missing values.
PART III: Effects of Measurement Error in Variables
The data set provided for this part of assignment is Measurement error that contains five variables: Y, Xl, X2, CY, and CX1. Y is a hypothetical outcome variable of interest, and Xl and X2 are predictors. While Y, X1, and X2 are assumed to be measured without measurement error (e.g., high reliability coefficients), CY and CX1 are variables that are contaminated by measurement error (e.g., low reliability coefficients). Please conduct the following set of analyses to investigate the effects of measurement error in variables.
1. Obtain the bivariate correlation coefficients for each pair below and compare the magnitude of the correlation coefficients:
Cor(Y,X1)
Cor(Y,CX1)
Cor(CY,CX1)
2. Examine the results carefully after fitting two multiple regression models (see, below) and discuss if there is any substantial change in the results (e.g., intercept, regression coefficients, standard errors, R2, F-ratio, p-values, etc) when the outcome variable contains measurement error.
a) Regress Y on Xl and X2.
b) Regress CY on Xl and X2.
3. Examine the results carefully after fitting two multiple regression models (see, below) and discuss if there is any substantial change in the results (e.g., intercept, regression coefficients, standard errors, R2, F-ratio, p-values, etc) when the predictor X1 variable contains measure¬ment error.
a) Regress Y on X1 and X2.
b) Regress Y on CX1 and X2.
Attachment:- Assignment Files.rar