The goal for today is to specify, fit and evaluate a path model with mediation. First, let’s load our packages:
# Load tidyverse and lavaan packages
library(tidyverse)
library(lavaan)Let’s load in the data:
# Load the data
leader <- read_csv("https://uoepsy.github.io/dapr3/2324/lectures/leader.csv")## Rows: 550 Columns: 6
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): ID
## dbl (5): leader, sleep, exercise, aggression, swb
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.# Preview the data
leader## # A tibble: 550 × 6
## ID leader sleep exercise aggression swb
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 participant1 0.9 4.7 5 0.36 0.47
## 2 participant2 -0.13 4 2 0.5 -0.2
## 3 participant3 -0.9 6 4 -0.61 0.3
## 4 participant4 0.15 5 3 0.02 0.58
## 5 participant5 1.18 4.1 4 0.4 0.28
## 6 participant6 0.69 4.1 3 -0.47 0.25
## 7 participant7 0.78 5.8 3 1.26 0.51
## 8 participant8 -1.69 3.7 4 -1.05 -0.17
## 9 participant9 0.23 2.8 3 0.39 -0.28
## 10 participant10 0.27 6.1 4 -0.39 -0.24
## # ℹ 540 more rowsLet’s specify a model:
# Define the model
path1 = '
aggression ~ leader
swb ~ aggression
swb ~ leader
swb ~ exercise + sleep
'What are we saying here? What are the relationships?
Now let’s estimate and view:
# Fit the model
path1_out <- sem(path1, data = leader)
# Print the model
summary(path1_out, # Model
fit.measures = T, # Fit indices
std = T
)## lavaan 0.6.16 ended normally after 2 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 7
##
## Number of observations 550
##
## Model Test User Model:
##
## Test statistic 3.152
## Degrees of freedom 2
## P-value (Chi-square) 0.207
##
## Model Test Baseline Model:
##
## Test statistic 574.763
## Degrees of freedom 7
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.998
## Tucker-Lewis Index (TLI) 0.993
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -629.036
## Loglikelihood unrestricted model (H1) -627.460
##
## Akaike (AIC) 1272.073
## Bayesian (BIC) 1302.242
## Sample-size adjusted Bayesian (SABIC) 1280.021
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.032
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.097
## P-value H_0: RMSEA <= 0.050 0.578
## P-value H_0: RMSEA >= 0.080 0.132
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.017
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## aggression ~
## leader 0.380 0.018 21.134 0.000 0.380 0.669
## swb ~
## aggression 0.416 0.047 8.772 0.000 0.416 0.401
## leader -0.028 0.027 -1.053 0.293 -0.028 -0.048
## exercise 0.182 0.018 9.912 0.000 0.182 0.337
## sleep 0.200 0.019 10.472 0.000 0.200 0.356
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .aggression 0.165 0.010 16.583 0.000 0.165 0.552
## .swb 0.204 0.012 16.583 0.000 0.204 0.633Now let’s add the mediation effects:
path1 = '
# Direct effects
aggression ~ a*leader # aggression (M) predicted by abusive leader behaviour (X)
swb ~ b*aggression # well-being (Y) predicted by aggression (M)
swb ~ c*leader # well-being (Y) predicted by leader abusive behaviour (X): direct effect
swb ~ exercise + sleep # covariates
# Mediation effects
indirect := a*b
total := (a*b)+c
'Estimate the model:
# Estimate the model
model1.est <- sem(path1, data = leader)
# Report the model
summary(model1.est,
fit.measures = T,
std = T,
modindices = T)## lavaan 0.6.16 ended normally after 2 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 7
##
## Number of observations 550
##
## Model Test User Model:
##
## Test statistic 3.152
## Degrees of freedom 2
## P-value (Chi-square) 0.207
##
## Model Test Baseline Model:
##
## Test statistic 574.763
## Degrees of freedom 7
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.998
## Tucker-Lewis Index (TLI) 0.993
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -629.036
## Loglikelihood unrestricted model (H1) -627.460
##
## Akaike (AIC) 1272.073
## Bayesian (BIC) 1302.242
## Sample-size adjusted Bayesian (SABIC) 1280.021
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.032
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.097
## P-value H_0: RMSEA <= 0.050 0.578
## P-value H_0: RMSEA >= 0.080 0.132
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.017
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## aggression ~
## leader (a) 0.380 0.018 21.134 0.000 0.380 0.669
## swb ~
## aggression (b) 0.416 0.047 8.772 0.000 0.416 0.401
## leader (c) -0.028 0.027 -1.053 0.293 -0.028 -0.048
## exercise 0.182 0.018 9.912 0.000 0.182 0.337
## sleep 0.200 0.019 10.472 0.000 0.200 0.356
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .aggression 0.165 0.010 16.583 0.000 0.165 0.552
## .swb 0.204 0.012 16.583 0.000 0.204 0.633
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## indirect 0.158 0.020 8.102 0.000 0.158 0.268
## total 0.130 0.021 6.072 0.000 0.130 0.220
##
## Modification Indices:
##
## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 leader ~~ leader 0.000 0.000 0.000 0.000 0.000
## 2 leader ~~ exercise 0.000 0.000 0.000 NA 0.000
## 3 leader ~~ sleep 0.000 0.000 0.000 NA 0.000
## 4 aggression ~ swb 1.075 -0.066 -0.066 -0.069 -0.069
## 5 aggression ~ exercise 0.145 0.006 0.006 0.012 0.012
## 6 aggression ~ sleep 3.061 -0.030 -0.030 -0.055 -0.055
## 7 leader ~ aggression 0.898 1.313 1.313 0.745 0.745
## 8 leader ~ swb 0.002 0.008 0.008 0.005 0.005
## 9 leader ~ exercise 0.000 0.000 0.000 0.000 0.000
## 10 leader ~ sleep 0.000 0.000 0.000 0.000 0.000
## 11 exercise ~ aggression 0.025 0.010 0.010 0.005 0.005
## 12 exercise ~ swb 0.029 0.027 0.027 0.014 0.014
## 13 exercise ~ leader 0.000 0.000 0.000 0.000 0.000
## 14 exercise ~ sleep 0.000 0.000 0.000 0.000 0.000
## 15 sleep ~ aggression 0.913 -0.056 -0.056 -0.030 -0.030
## 16 sleep ~ swb 1.052 -0.155 -0.155 -0.087 -0.087
## 17 sleep ~ leader 0.000 0.000 0.000 0.000 0.000
## 18 sleep ~ exercise 0.000 0.000 0.000 0.000 0.000Now we want to compute some confidence intervals for the indirect effects:
# Estimate the model
model2.est <- sem(path1, data = leader, se = 'bootstrap')
# Report the model
summary(model1.est,
fit.measures = T,
ci = T,
std = T,
modindices = T)## lavaan 0.6.16 ended normally after 2 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 7
##
## Number of observations 550
##
## Model Test User Model:
##
## Test statistic 3.152
## Degrees of freedom 2
## P-value (Chi-square) 0.207
##
## Model Test Baseline Model:
##
## Test statistic 574.763
## Degrees of freedom 7
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.998
## Tucker-Lewis Index (TLI) 0.993
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -629.036
## Loglikelihood unrestricted model (H1) -627.460
##
## Akaike (AIC) 1272.073
## Bayesian (BIC) 1302.242
## Sample-size adjusted Bayesian (SABIC) 1280.021
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.032
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.097
## P-value H_0: RMSEA <= 0.050 0.578
## P-value H_0: RMSEA >= 0.080 0.132
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.017
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## aggression ~
## leader (a) 0.380 0.018 21.134 0.000 0.345 0.415
## swb ~
## aggression (b) 0.416 0.047 8.772 0.000 0.323 0.509
## leader (c) -0.028 0.027 -1.053 0.293 -0.081 0.024
## exercise 0.182 0.018 9.912 0.000 0.146 0.219
## sleep 0.200 0.019 10.472 0.000 0.162 0.237
## Std.lv Std.all
##
## 0.380 0.669
##
## 0.416 0.401
## -0.028 -0.048
## 0.182 0.337
## 0.200 0.356
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .aggression 0.165 0.010 16.583 0.000 0.146 0.185
## .swb 0.204 0.012 16.583 0.000 0.180 0.229
## Std.lv Std.all
## 0.165 0.552
## 0.204 0.633
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## indirect 0.158 0.020 8.102 0.000 0.120 0.196
## total 0.130 0.021 6.072 0.000 0.088 0.172
## Std.lv Std.all
## 0.158 0.268
## 0.130 0.220
##
## Modification Indices:
##
## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 leader ~~ leader 0.000 0.000 0.000 0.000 0.000
## 2 leader ~~ exercise 0.000 0.000 0.000 NA 0.000
## 3 leader ~~ sleep 0.000 0.000 0.000 NA 0.000
## 4 aggression ~ swb 1.075 -0.066 -0.066 -0.069 -0.069
## 5 aggression ~ exercise 0.145 0.006 0.006 0.012 0.012
## 6 aggression ~ sleep 3.061 -0.030 -0.030 -0.055 -0.055
## 7 leader ~ aggression 0.898 1.313 1.313 0.745 0.745
## 8 leader ~ swb 0.002 0.008 0.008 0.005 0.005
## 9 leader ~ exercise 0.000 0.000 0.000 0.000 0.000
## 10 leader ~ sleep 0.000 0.000 0.000 0.000 0.000
## 11 exercise ~ aggression 0.025 0.010 0.010 0.005 0.005
## 12 exercise ~ swb 0.029 0.027 0.027 0.014 0.014
## 13 exercise ~ leader 0.000 0.000 0.000 0.000 0.000
## 14 exercise ~ sleep 0.000 0.000 0.000 0.000 0.000
## 15 sleep ~ aggression 0.913 -0.056 -0.056 -0.030 -0.030
## 16 sleep ~ swb 1.052 -0.155 -0.155 -0.087 -0.087
## 17 sleep ~ leader 0.000 0.000 0.000 0.000 0.000
## 18 sleep ~ exercise 0.000 0.000 0.000 0.000 0.000