Couples/Optimism Homework

Rose Maier, 4/28/14
I'm using lavaan. Here's an example of mediation in lavaan: http://lavaan.ugent.be/tutorial/mediation.html

# Make sure to set working directory to wherever the data file is saved.
data <- read.delim("optimismclose.txt", header = F, sep = "\t")

# assign variable names, since they're not included in the data file
colnames(data) <- c("mlot", "mmq", "mcss", "flot", "fmq", "fcss")

# checking for missing values. turns out there are none, so no action
# needed.
check <- apply(data, 2, is.nan)

summary(data[, 4:6])  # double checking the ranges on the variables, to see if they look sensible (e.g. no -12345 values)

##       flot           fmq            fcss     
##  Min.   :16.0   Min.   :15.3   Min.   :1.38  
##  1st Qu.:25.0   1st Qu.:26.6   1st Qu.:3.97  
##  Median :29.5   Median :29.1   Median :4.38  
##  Mean   :29.4   Mean   :28.7   Mean   :4.29  
##  3rd Qu.:34.0   3rd Qu.:31.3   3rd Qu.:4.75  
##  Max.   :40.0   Max.   :35.0   Max.   :5.00

A model in which the effect of females' optimism (FLOT) on females' relationship satisfaction (FCSS) is fully mediated by females' perceived support (FMQ).

library(lavaan)

## This is lavaan 0.5-16
## lavaan is BETA software! Please report any bugs.

model1 <- "\n   # regressions\n     fcss ~ fmq\n     fmq ~ flot\n"
fit1 <- sem(model1, data = data)

# This second model is equivalent, but it asks R to calculate the indirect
# effect for me.
model1 <- "\n   # regressions\n     fcss ~ b*fmq\n     fmq ~ a*flot\n   # indirect effect\n     ab := a*b\n"
fit1 <- sem(model1, data = data)
summary(fit1, standardized = TRUE)

## lavaan (0.5-16) converged normally after  15 iterations
## 
##   Number of observations                           108
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic                2.479
##   Degrees of freedom                                 1
##   P-value (Chi-square)                           0.115
## 
## Parameter estimates:
## 
##   Information                                 Expected
##   Standard Errors                             Standard
## 
##                    Estimate  Std.err  Z-value  P(>|z|)   Std.lv  Std.all
## Regressions:
##   fcss ~
##     fmq       (b)     0.105    0.013    8.137    0.000    0.105    0.617
##   fmq ~
##     flot      (a)     0.173    0.063    2.770    0.006    0.173    0.258
## 
## Variances:
##     fcss              0.263    0.036                      0.263    0.620
##     fmq              13.632    1.855                     13.632    0.934
## 
## Defined parameters:
##     ab                0.018    0.007    2.622    0.009    0.018    0.159

# The argument standardized=TRUE augments the output with standardized
# parameter values. Two extra columns of standardized parameter values are
# printed. In the first column (labeled Std.lv), only the latent variables
# are standardized. In the second column (labeled Std.all), both latent and
# observed variables are standardized. The latter is often called the
# ‘completely standardized solution’.

What is the mediated (indirect) effect of FLOT on FCSS (via FMQ)? Give both the undstandardized and fully standardized effect sizes.

The unstandardized effect of FLOT on FCSS via FMQ is 0.018. The standardized estimate is 0.159.

Can you reject the null hypothesis that the mediated effect is zero?

Yep! The Z-test of the indirect effect is significant (Z = 2.622, p = .009), but of course this is based on the assumption that the direct effect is zero.

What is the model-implied total effect of FLOT on FCSS?

In this case, the model specifies that the direct effect of FLOT on FCSS is 0, so the total effect is equal to the indirect effect (a*b) = 0.018.

A model which includes both a direct effect of FLOT->FCSS and an effect that is mediated by FMQ.

model2 <- "\n   # regressions\n     fcss ~ fmq\n     fmq ~ flot\n     fcss ~ flot\n"
fit2 <- sem(model2, data = data)

# This second model is equivalent, but it asks R to calculate the indirect
# and total effects for me.
model2 <- "\n   # regressions\n     fcss ~ c*flot\n     fcss ~ b*fmq\n     fmq ~ a*flot\n   # indirect effect\n     ab := a*b\n   # total effect\n     total := c + (a*b)\n"
fit2 <- sem(model2, data = data)
summary(fit2, standardized = TRUE)

## lavaan (0.5-16) converged normally after  18 iterations
## 
##   Number of observations                           108
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic                0.000
##   Degrees of freedom                                 0
##   P-value (Chi-square)                           0.000
## 
## Parameter estimates:
## 
##   Information                                 Expected
##   Standard Errors                             Standard
## 
##                    Estimate  Std.err  Z-value  P(>|z|)   Std.lv  Std.all
## Regressions:
##   fcss ~
##     flot      (c)     0.014    0.009    1.583    0.113    0.014    0.123
##     fmq       (b)     0.100    0.013    7.546    0.000    0.100    0.585
##   fmq ~
##     flot      (a)     0.173    0.063    2.770    0.006    0.173    0.258
## 
## Variances:
##     fcss              0.257    0.035                      0.257    0.606
##     fmq              13.632    1.855                     13.632    0.934
## 
## Defined parameters:
##     ab                0.017    0.007    2.600    0.009    0.017    0.151
##     total             0.031    0.011    2.954    0.003    0.031    0.273

What is the mediated (indirect) effect of FLOT on FCSS (via FMQ)? Give both the undstandardized and fully standardized effect sizes.

The unstandardized effect of FLOT on FCSS via FMQ is 0.017. The standardized estimate is 0.151.

Can you reject the null hypothesis that the mediated effect is zero?

Yep! The Z-test of the indirect effect is significant (Z = 2.600, p = .009).

What is the model-implied total effect of FLOT on FCSS?

The total effect of FLOT on FCSS is the direct effect plus the indirect effect = 0.031 (unstandardized) or 0.273 (standardized).