HW5
Your Name
library(lavaan)
library(semPlot)
speed <- read.csv("C:/Users/johna/OneDrive/Documents/speeddate_mod.csv")
nlsy <- read.csv("C:/Users/johna/OneDrive/Documents/nlsy_med.csv")Question 1: Moderation Analysis (Speed Dating Data)
Fisman, Iyengar, Kamenica, and Simonson (2006) ran a large speed-dating experiment where participants rated their partners on several traits, including attractiveness, intelligence, and overall likability. All ratings were given on a 10-point scale.
In this analysis, we test whether perceived intelligence moderates the relationship between perceived attractiveness and overall likability.
1) Remove rows containing missing values
speed <- read.csv("speeddate_mod.csv")
# remove rows with missing values
speed_complete <- na.omit(speed)
head(speed_complete)## X other_like other_attr other_intel
## 1 1 7 8 9
## 2 2 8 8 4
## 3 3 8 8 8
## 4 4 7 7 7
## 5 5 7 8 7
## 6 6 7 6 10This removes any observations with missing values so that the analyses use only complete cases.
2) Moderation analysis
To test moderation, we include an interaction term between attractiveness and intelligence.
model_mod <- lm(other_like ~ other_attr * other_intel, data = speed_complete)
summary(model_mod)##
## Call:
## lm(formula = other_like ~ other_attr * other_intel, data = speed_complete)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.9241 -0.7147 0.0759 0.7249 6.3658
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.791311 0.446842 -1.771 0.0768 .
## other_attr 0.657284 0.076975 8.539 < 2e-16 ***
## other_intel 0.488173 0.059996 8.137 8.42e-16 ***
## other_attr:other_intel -0.017145 0.009832 -1.744 0.0814 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.248 on 1505 degrees of freedom
## Multiple R-squared: 0.5354, Adjusted R-squared: 0.5345
## F-statistic: 578.2 on 3 and 1505 DF, p-value: < 2.2e-16Interpretation
The interaction term other_attr:other_intel tells us whether intelligence changes the relationship between attractiveness and likability.
Looking at the regression output, the interaction term is not statistically significant (p > .05). This suggests that intelligence does not significantly moderate the relationship between attractiveness and how much someone is liked.
In other words, attractiveness seems to influence likability in a similar way regardless of the perceived intelligence of the partner.
3) Moderation analysis after centering variables
Next, we center attractiveness and intelligence before creating the interaction term.
speed_complete$attr_c <- scale(speed_complete$other_attr, center = TRUE, scale = FALSE)
speed_complete$intel_c <- scale(speed_complete$other_intel, center = TRUE, scale = FALSE)
model_center <- lm(other_like ~ attr_c * intel_c, data = speed_complete)
summary(model_center)##
## Call:
## lm(formula = other_like ~ attr_c * intel_c, data = speed_complete)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.9241 -0.7147 0.0759 0.7249 6.3658
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.215414 0.033687 184.503 <2e-16 ***
## attr_c 0.528312 0.017921 29.480 <2e-16 ***
## intel_c 0.379965 0.024185 15.711 <2e-16 ***
## attr_c:intel_c -0.017145 0.009832 -1.744 0.0814 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.248 on 1505 degrees of freedom
## Multiple R-squared: 0.5354, Adjusted R-squared: 0.5345
## F-statistic: 578.2 on 3 and 1505 DF, p-value: < 2.2e-16Interpretation
After centering the variables, the interaction term is still not statistically significant.
This means that centering the predictors did not change the conclusion of the moderation test. Centering mainly helps with interpretation and can reduce multicollinearity, but it does not change the underlying relationship between the variables.
Question 2: Mediation Analysis (NLSY Data)
Davis-Kean (2005) suggested that parents’ education may influence children’s academic achievement indirectly through the home environment.
Here we test whether Home Environment (HE) mediates the relationship between Mother’s Education (ME) and children’s math achievement (Math).
1) Conduct mediation analysis with bootstrapping
nlsy <- read.csv("nlsy_med.csv")
model_med <- '
# path from ME to HE
HE ~ a*ME
# paths predicting math
math ~ b*HE + cprime*ME
# indirect effect
ab := a*b
# total effect
total := cprime + (a*b)
'
fit_med <- sem(model_med,
data = nlsy,
se = "bootstrap",
bootstrap = 5000)## Warning: lavaan->lav_model_nvcov_bootstrap():
## 22 bootstrap runs failed or did not converge.summary(fit_med, standardized = TRUE, ci = TRUE)## lavaan 0.6-21 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 5
##
## Number of observations 371
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Parameter Estimates:
##
## Standard errors Bootstrap
## Number of requested bootstrap draws 5000
## Number of successful bootstrap draws 4978
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## HE ~
## ME (a) 0.139 0.041 3.437 0.001 0.060 0.218
## math ~
## HE (b) 0.465 0.126 3.687 0.000 0.222 0.720
## ME (cprm) 0.463 0.118 3.939 0.000 0.226 0.693
## Std.lv Std.all
##
## 0.139 0.166
##
## 0.465 0.165
## 0.463 0.196
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .HE 2.724 0.206 13.214 0.000 2.323 3.130
## .math 20.621 2.900 7.111 0.000 15.536 26.843
## Std.lv Std.all
## 2.724 0.972
## 20.621 0.924
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.065 0.025 2.610 0.009 0.024 0.120
## total 0.528 0.119 4.425 0.000 0.286 0.761
## Std.lv Std.all
## 0.065 0.027
## 0.528 0.2232) Are the effects significant? Does mediation exist?
There are three main effects to look at:
- a path: ME → HE
- c′ path: ME → math (direct effect controlling for
HE)
- ab: the indirect effect through the home environment
Based on the output:
- The a path is significant, meaning mothers with higher education tend to provide better home environments.
- The b path is significant, meaning the home environment is related to children’s math achievement.
- The indirect effect (ab) is significant based on the bootstrap confidence interval.
- The direct effect (c′) is also still significant.
Conclusion
Because both the direct effect (c′) and the indirect effect (ab) are significant, this indicates partial mediation.
This means that mothers’ education affects children’s math scores both directly and indirectly through the home environment.
3) Display the path plot
semPaths(fit_med,
what = "std",
layout = "tree",
edge.label.cex = 1.2,
sizeMan = 7,
nCharNodes = 0)
The diagram shows the relationships between the three variables:
- ME → HE (path a)
- HE → math (path b)
- ME → math (direct path c′)
The indirect pathway ME → HE → math represents the mediation effect.
References
Davis-Kean, P. E. (2005). The influence of parent education and family income on child achievement: The indirect role of parental expectations and the home environment. Journal of Family Psychology, 19(2), 294–304.
Fisman, R., Iyengar, S. S., Kamenica, E., & Simonson, I. (2006). Gender differences in mate selection: Evidence from a speed dating experiment. Quarterly Journal of Economics, 121, 673–697.