library(seminr)
library(dplyr)
data <- openxlsx::read.xlsx("MMM_influencer_data.xlsx")MMM WT 2023/24: Exercise 6
Set-up
Load relevant packages.
(If necessary) do all relevant steps from the last exercise.
- transform WTP to a numeric variable
- set up the model (mm and sm)
- estimate the model (model)
- summarize the estimated model (model_sum)
data$WP01_01_num <- gsub(pattern = ",", replacement = ".", data$WP01_01) %>%
as.numeric()
# Model set up
## Measurement model
mm <- constructs(
composite("SIC", multi_items("SC02_0", 1:7)),
composite("PL", multi_items("PL01_0", c(1, 4, 6, 7))),
composite("PQ", multi_items("PQ01_0", 1:4)),
composite("PI", multi_items("PI01_0", c(1, 2, 4, 5, 6))),
composite("WTP", single_item("WP01_01_num"))
)
## Structural model
sm <- relationships(
paths(from = "SIC", to = c("PL", "PQ", "PI")),
paths(from = "PL", to = "PI"),
paths(from = "PQ", to = "PI"),
paths(from = "PI", to = "WTP"))
# Estimate the model:
model <- estimate_pls(data = data,
measurement_model = mm,
structural_model = sm,
inner_weights = path_weighting)Generating the seminr modelAll 223 observations are valid.# Summarize the model
model_sum <- summary(model)structural model assessment
We work with out full model again.
bootstrap the model and summarize the bootstrapped model
model_boot <- bootstrap_model(
seminr_model = model,
nboot = 1000, # number of bootstrap iterations
cores = parallel::detectCores(), # use all cores
seed = 1001)Bootstrapping model using seminr...SEMinR Model successfully bootstrappedmodel_boot_sum <- summary(model_boot)step 1: collinearity in the structural model (again)
model_sum$vif_antecedentsPL :
SIC
.
PQ :
SIC
.
PI :
SIC PL PQ
1.274 2.354 2.221
WTP :
PI
. Show an interpretation
# The VIFs are all below 5 --> Thus, no collinearity problem among exogenous constructs.step 2: path coefficients
direct paths
model_boot_sum$bootstrapped_paths Original Est. Bootstrap Mean Bootstrap SD T Stat. 2.5% CI 97.5% CI
SIC -> PL 0.454 0.457 0.050 9.146 0.356 0.548
SIC -> PQ 0.398 0.401 0.053 7.468 0.292 0.501
SIC -> PI 0.044 0.043 0.058 0.761 -0.069 0.155
PL -> PI 0.654 0.654 0.057 11.568 0.540 0.771
PQ -> PI 0.145 0.144 0.056 2.587 0.030 0.244
PI -> WTP 0.441 0.445 0.051 8.715 0.344 0.540Show an interpretation
# All but one relationship is positive and significant. Specifically:
## SIC has a positive and significant impact on PL (path coefficient = 0.454, t = 9.146, CI95% = [0.356; 0.548])
## SIC has a positive and significant impact on PQ (path coefficient = 0.398, t = 7.468, CI95% = [0.292; 0.501])
## PL has a positive and significant impact on PI (path coefficient = 0.654, t =11.568, CI95% = [0.540; 0.771]) # highest impact of PI's antecedents on PI
## PQ has a positive and significant impact on PI (path coefficient = 0.145, t = 2.587, CI95% = [0.030; 0.244])
## PI has a positive and significant impact on WTP (path coefficient = 0.441, t = 8.715, CI95% = [0.344; 0.540])
## SIC does not have a significant impact on PI (path coefficient = 0.044, t = 0.761, CI95% = [-0.069; 0.155])total effects
Total effects are the products of it’s antecedent paths (–> see mediation analysis)
model_boot_sum$bootstrapped_total_paths Original Est. Bootstrap Mean Bootstrap SD T Stat. 2.5% CI 97.5% CI
SIC -> PL 0.454 0.457 0.050 9.146 0.356 0.548
SIC -> PQ 0.398 0.401 0.053 7.468 0.292 0.501
SIC -> PI 0.399 0.399 0.067 5.922 0.254 0.529
SIC -> WTP 0.176 0.178 0.036 4.882 0.109 0.252
PL -> PI 0.654 0.654 0.057 11.568 0.540 0.771
PL -> WTP 0.288 0.291 0.043 6.767 0.208 0.373
PQ -> PI 0.145 0.144 0.056 2.587 0.030 0.244
PQ -> WTP 0.064 0.064 0.026 2.444 0.013 0.118
PI -> WTP 0.441 0.445 0.051 8.715 0.344 0.540Show an interpretation
# All relationships are positive and significant.
## SIC has a positive and significant impact on PL (total effect = 0.454, t = 9.146, CI95% = [0.356; 0.548])
## SIC has a positive and significant impact on PQ (total effect = 0.398, t = 7.468, CI95% = [0.292; 0.501])
## SIC has a positive and significant impact on PI (total effect = 0.399, t = 5.922, CI95% = [0.254; 0.529])
## SIC has a positive and significant impact on WTP (total effect = 0.176, t = 4.882, CI95% = [0.109; 0.252])
## PL has a positive and significant impact on PI (total effect = 0.654, t = 11.568, CI95% = [0.540; 0.771])
## PL has a positive and significant impact on WTP (total effect = 0.288, t = 6.767, CI95% = [0.208; 0.373])
## PQ has a positive and significant impact on PI (total effect = 0.145, t = 2.587, CI95% = [0.030; 0.244])
## PQ has a positive and significant impact on WTP (total effect = 0.064, t = 2.444, CI95% = [0.013; 0.118])
## PI has a positive and significant impact on WTP (total effect = 0.441, t = 8.715, CI95% = [0.344; 0.540])
# PI antecedent with highest impact on WTP = PL.revisit: revisit the model’s HTMT with bootstrap
model_boot_sum$bootstrapped_HTMT Original Est. Bootstrap Mean Bootstrap SD T Stat. 2.5% CI 97.5% CI
SIC -> PL 0.476 0.474 0.055 8.677 0.360 0.576
SIC -> PQ 0.413 0.412 0.060 6.917 0.290 0.522
SIC -> PI 0.423 0.420 0.073 5.792 0.257 0.556
SIC -> WTP 0.140 0.154 0.055 2.541 0.072 0.286
PL -> PQ 0.785 0.784 0.038 20.832 0.700 0.848
PL -> PI 0.825 0.824 0.026 32.306 0.772 0.868
PL -> WTP 0.463 0.470 0.048 9.712 0.384 0.566
PQ -> PI 0.682 0.681 0.040 17.222 0.598 0.748
PQ -> WTP 0.485 0.491 0.046 10.575 0.398 0.582
PI -> WTP 0.449 0.454 0.052 8.619 0.350 0.553Show an interpretation
# The HTMT indicates lacking discriminant validity for PL and PI since CI includes 0.85.
# All other upper CI limits are below 0.85.