Does Leaders’ Behaviour Drive Subordinates’ Innovativeness?
Study 3
- 26 Pax - Reducing Item List - With IWB
Study 3 - 26 Pax - Reducing Item List - With IWB
Updated by Uwe H Kaufmann on 25 Jul 2022, 06:35h, Singapore
- 1 Preparing Data
- 2 Studying Data
- 3 Showing Graphs of Data
- 3.1 Plot Histograms of all Variables
- 3.2 Show Error Plot of Items per Factor
- 3.3 Show Item List
- 3.4 Plot Correlation Matrix of Items
- 3.5 Plot Correlation Matrix of Behaviours
- 3.6 Plot Correlation Matrix of Behaviours with p-value
- 3.7 Plot Correlation Matrix of Factors
- 3.8 Plot Correlation Matrix of Factor Items
- 4 Testing Whether ILS Scale of Study 2 is Confirmed in Study 3 - 287 Raters
- 5 Testing Whether ILS Factors
Influence IWB - 76 Raters
- 5.1 How to Evaluate SEM Output?
- 5.2 About Estimators
- 5.3 Build Model: Head -> Hand -> IWB with Heart as Mediator (MLR) - 76 Raters
- 5.4 Plot Model (MLR) - 76 Raters
- 5.5 Build Model: Head -> Hand -> IWB with Heart as Mediator (WLSMV) - 76 Raters
- 5.6 Plot Model (WLSMV) - 76 Raters
- 5.7 Build Model: Head -> Hand -> IWB with Heart as Mediator (DWLS) - 76 Raters
- 5.8 Plot Model - (DWLS) 76 Raters
1 Preparing Data
1.1 Load Libraries
## Necessary Libraries loaded.1.2 Load Data for Organisation with 26 Ratees and 287 Raters
## Stacked data with 78 Raters including IWB loaded.1.3 Unstack and Clean Data
## Data unstacked and prepared for Analysis. Blank cells have been filled with Column Mean.1.4 Eliminate Items
# Making New Data Set
ReduceBy <- c("SN06", "SN19", "SN29")
ItemsToCut <- paste(ReduceBy, collapse = ", ")
cat("Dataset reduced by items", ItemsToCut, "due to low factor loading or cross loading. \nAll behaviours stay represented.")## Dataset reduced by items SN06, SN19, SN29 due to low factor loading or cross loading.
## All behaviours stay represented.# Keep full data set
dfValFull <- dfVal
# Reduce data sets
dfUnstack <- select(dfUnstack, -c(all_of(ReduceBy)))
dfVal <- select(dfVal, -c(all_of(ReduceBy)))
dfValNoIWB <- select(dfValNoIWB, -c(all_of(ReduceBy)))
# Delete support variables
rm(ItemsToCut, ReduceBy)
# Write
setwd("~/AB PRIVATE/01 Amy/AB Amy PhD/Part 3/Data/Study3")
write.csv(dfUnstack, file = paste(today, "UnStackedData3reduced.csv"))1.5 Make Factor and Behaviour Variables
## Behaviour and Factor Data generated out of Item Means.2 Studying Data
2.1 Displaying Descriptive Stats
Kurtosis and Skewness are used as indication of presence of normality in the data. If the data are normal Kurtosis and Skewness are within -2 and +2. The closer the 0 the better.
# Loading necessary packages
if(! "vtable" %in% installed.packages()) { install.packages("vtable", dependencies = TRUE) }
library(vtable)
if(! "moments" %in% installed.packages()) { install.packages("moments", dependencies = TRUE) }
library(moments)
ST <- as.data.frame(sumtable(dfVal[c(01:31)], out = 'return', title='Summary Statistics by Item', digits = 3, fixed.digits = TRUE,
summ = list(
c('notNA(x)','mean(x)','sd(x)','min(x)', 'pctile(x)[25]', 'median(x)', 'pctile(x)[75]', 'max(x)', 'kurtosis(x)', 'skewness(x)')
),
summ.names = list(
c('N','Mean','SD','Min', '25%', 'Median', '75%', 'Max', 'Kurtosis', 'Skewness')
)
))
formattable(ST, caption = "Summary Statistics by Item - ILS", align = c("l", "c", "c", "c", "c", "c", "c", "c", "c", "c", "c"), list(
Mean = color_tile("pink", "green"),
Cosigned = formatter("span",
style = x ~ style(
"border-radius" = "4px",
"padding-right" = "4px",
"background-color" = sapply(x,bg.picker)),
x ~ sprintf("%.2f (rank: %02d)", x, rank(-x)))
))| Variable | N | Mean | SD | Min | 25% | Median | 75% | Max | Kurtosis | Skewness |
|---|---|---|---|---|---|---|---|---|---|---|
| SN01 | 76 | 6.054 | 1.057 | 2 | 6.000 | 6 | 7.000 | 7 | 5.902 | -1.610 |
| SN02 | 76 | 5.724 | 1.173 | 2 | 5.000 | 6 | 7.000 | 7 | 4.069 | -1.047 |
| SN03 | 76 | 5.849 | 1.041 | 2 | 5.000 | 6 | 7.000 | 7 | 4.214 | -1.045 |
| SN04 | 76 | 5.893 | 1.173 | 2 | 5.670 | 6 | 7.000 | 7 | 5.701 | -1.539 |
| SN05 | 76 | 5.986 | 1.064 | 2 | 6.000 | 6 | 7.000 | 7 | 6.490 | -1.641 |
| SN07 | 76 | 5.901 | 1.121 | 2 | 5.901 | 6 | 7.000 | 7 | 4.329 | -1.228 |
| SN08 | 76 | 5.806 | 1.041 | 2 | 5.000 | 6 | 6.250 | 7 | 4.846 | -1.167 |
| SN09 | 76 | 5.877 | 1.006 | 2 | 5.000 | 6 | 7.000 | 7 | 6.841 | -1.487 |
| SN10 | 76 | 5.740 | 1.096 | 2 | 5.000 | 6 | 6.000 | 7 | 4.312 | -1.116 |
| SN11 | 76 | 5.736 | 1.020 | 2 | 5.000 | 6 | 6.000 | 7 | 4.935 | -1.189 |
| SN12 | 76 | 6.013 | 1.039 | 2 | 6.000 | 6 | 7.000 | 7 | 5.320 | -1.390 |
| SN13 | 76 | 6.040 | 1.012 | 2 | 6.000 | 6 | 7.000 | 7 | 6.487 | -1.632 |
| SN14 | 76 | 6.408 | 0.751 | 4 | 6.000 | 7 | 7.000 | 7 | 4.092 | -1.201 |
| SN15 | 76 | 6.013 | 0.973 | 2 | 6.000 | 6 | 7.000 | 7 | 5.482 | -1.251 |
| SN16 | 76 | 6.184 | 0.934 | 2 | 6.000 | 6 | 7.000 | 7 | 6.896 | -1.559 |
| SN17 | 76 | 6.133 | 1.062 | 2 | 6.000 | 6 | 7.000 | 7 | 5.379 | -1.478 |
| SN18 | 76 | 5.867 | 1.215 | 2 | 5.000 | 6 | 7.000 | 7 | 4.380 | -1.270 |
| SN20 | 76 | 5.961 | 1.101 | 2 | 6.000 | 6 | 7.000 | 7 | 4.726 | -1.310 |
| SN21 | 76 | 5.946 | 0.992 | 2 | 6.000 | 6 | 7.000 | 7 | 5.888 | -1.458 |
| SN22 | 76 | 5.886 | 1.027 | 2 | 5.886 | 6 | 6.250 | 7 | 5.632 | -1.472 |
| SN23 | 76 | 6.184 | 0.976 | 2 | 6.000 | 6 | 7.000 | 7 | 6.383 | -1.588 |
| SN24 | 76 | 5.889 | 1.090 | 2 | 5.889 | 6 | 7.000 | 7 | 4.643 | -1.266 |
| SN25 | 76 | 6.027 | 1.107 | 1 | 6.000 | 6 | 7.000 | 7 | 7.578 | -1.774 |
| SN26 | 76 | 6.108 | 1.053 | 2 | 6.000 | 6 | 7.000 | 7 | 6.007 | -1.599 |
| SN27 | 76 | 5.920 | 1.105 | 2 | 6.000 | 6 | 7.000 | 7 | 5.462 | -1.573 |
| SN28 | 76 | 5.959 | 1.064 | 2 | 5.000 | 6 | 7.000 | 7 | 4.513 | -1.122 |
| SN30 | 76 | 6.243 | 0.921 | 2 | 6.000 | 6 | 7.000 | 7 | 7.994 | -1.847 |
| SN31 | 76 | 6.147 | 1.029 | 2 | 6.000 | 6 | 7.000 | 7 | 6.129 | -1.629 |
| SN32 | 76 | 5.931 | 1.181 | 2 | 5.931 | 6 | 7.000 | 7 | 5.105 | -1.475 |
| SN33 | 76 | 6.054 | 1.106 | 2 | 6.000 | 6 | 7.000 | 7 | 5.111 | -1.476 |
| SN34 | 76 | 6.027 | 1.019 | 2 | 6.000 | 6 | 7.000 | 7 | 5.624 | -1.422 |
ST <- as.data.frame(sumtable(dfVal[c(32:40)], out = 'return', title='Summary Statistics by Item', digits = 3, fixed.digits = TRUE,
summ = list(
c('notNA(x)','mean(x)','sd(x)','min(x)', 'pctile(x)[25]', 'median(x)', 'pctile(x)[75]', 'max(x)', 'kurtosis(x)', 'skewness(x)')
),
summ.names = list(
c('N','Mean','SD','Min', '25%', 'Median', '75%', 'Max', 'Kurtosis', 'Skewness')
)
))
formattable(ST, caption = "Summary Statistics by Item - IWB", align = c("l", "c", "c", "c", "c", "c", "c", "c", "c", "c", "c"), list(
Mean = color_tile("pink", "green"),
Cosigned = formatter("span",
style = x ~ style(
"border-radius" = "4px",
"padding-right" = "4px",
"background-color" = sapply(x,bg.picker)),
x ~ sprintf("%.2f (rank: %02d)", x, rank(-x)))
))| Variable | N | Mean | SD | Min | 25% | Median | 75% | Max | Kurtosis | Skewness |
|---|---|---|---|---|---|---|---|---|---|---|
| IWB01 | 76 | 5.421 | 1.086 | 2 | 5 | 6 | 6.000 | 7 | 4.224 | -0.958 |
| IWB02 | 76 | 5.421 | 1.099 | 2 | 5 | 5 | 6.000 | 7 | 3.925 | -0.709 |
| IWB03 | 76 | 5.513 | 1.113 | 3 | 5 | 6 | 6.000 | 7 | 2.314 | -0.296 |
| IWB04 | 76 | 4.592 | 0.955 | 2 | 4 | 5 | 5.000 | 6 | 2.565 | -0.312 |
| IWB05 | 76 | 4.855 | 1.029 | 2 | 4 | 5 | 6.000 | 7 | 3.309 | -0.521 |
| IWB06 | 76 | 4.303 | 1.132 | 1 | 4 | 4 | 5.000 | 6 | 2.967 | -0.447 |
| IWB07 | 76 | 4.816 | 1.092 | 2 | 4 | 5 | 6.000 | 7 | 2.645 | -0.496 |
| IWB08 | 76 | 4.763 | 1.094 | 1 | 4 | 5 | 5.250 | 7 | 4.189 | -0.689 |
| IWB09 | 76 | 4.697 | 1.108 | 1 | 4 | 5 | 5.000 | 7 | 3.852 | -0.803 |
ST <- as.data.frame(sumtable(dfBeh[c(01:11)], out = 'return', title='Summary Statistics by Behaviour', digits = 3, fixed.digits = TRUE,
summ = list(
c('notNA(x)','mean(x)','sd(x)','min(x)', 'pctile(x)[25]', 'median(x)', 'pctile(x)[75]', 'max(x)', 'kurtosis(x)', 'skewness(x)')
),
summ.names = list(
c('N','Mean','SD','Min', '25%', 'Median', '75%', 'Max', 'Kurtosis', 'Skewness')
)
))
formattable(ST, caption = "Summary Statistics by Behaviour - ILS", align = c("l", "c", "c", "c", "c", "c", "c", "c", "c", "c", "c"), list(
Mean = color_tile("pink", "green"),
Cosigned = formatter("span",
style = x ~ style(
"border-radius" = "4px",
"padding-right" = "4px",
"background-color" = sapply(x,bg.picker)),
x ~ sprintf("%.2f (rank: %02d)", x, rank(-x)))
))| Variable | N | Mean | SD | Min | 25% | Median | 75% | Max | Kurtosis | Skewness |
|---|---|---|---|---|---|---|---|---|---|---|
| B01 | 76 | 5.889 | 1.057 | 2.000 | 5.500 | 6.000 | 6.500 | 7 | 5.149 | -1.417 |
| B02 | 76 | 5.910 | 1.001 | 2.000 | 5.658 | 6.000 | 6.667 | 7 | 5.737 | -1.427 |
| B03 | 76 | 5.861 | 0.973 | 2.000 | 5.594 | 6.000 | 6.417 | 7 | 6.096 | -1.458 |
| B04 | 76 | 5.830 | 0.973 | 2.000 | 5.583 | 6.000 | 6.333 | 7 | 5.866 | -1.475 |
| B05 | 76 | 6.202 | 0.768 | 3.667 | 6.000 | 6.333 | 7.000 | 7 | 4.290 | -1.130 |
| B06 | 76 | 6.013 | 1.007 | 2.000 | 5.667 | 6.000 | 7.000 | 7 | 5.549 | -1.436 |
| B07 | 76 | 5.994 | 0.929 | 2.000 | 5.750 | 6.125 | 6.562 | 7 | 6.790 | -1.698 |
| B08 | 76 | 6.008 | 0.983 | 1.667 | 5.667 | 6.333 | 6.667 | 7 | 7.183 | -1.742 |
| B09 | 76 | 5.940 | 1.036 | 2.000 | 5.500 | 6.000 | 7.000 | 7 | 5.216 | -1.360 |
| B10 | 76 | 6.195 | 0.937 | 2.000 | 6.000 | 6.122 | 7.000 | 7 | 7.772 | -1.886 |
| B11 | 76 | 6.004 | 1.007 | 2.000 | 5.667 | 6.000 | 7.000 | 7 | 5.905 | -1.537 |
ST <- as.data.frame(sumtable(dfFac, out = 'return', title='Summary Statistics by Factor', digits = 3, fixed.digits = TRUE,
summ = list(
c('notNA(x)','mean(x)','sd(x)','min(x)', 'pctile(x)[25]', 'median(x)', 'pctile(x)[75]', 'max(x)', 'kurtosis(x)', 'skewness(x)')
),
summ.names = list(
c('N','Mean','SD','Min', '25%', 'Median', '75%', 'Max', 'Kurtosis', 'Skewness')
)
))
formattable(ST, caption = "Summary Statistics by Factor - ILS and IWB", align = c("l", "c", "c", "c", "c", "c", "c", "c", "c", "c", "c"), list(
Mean = color_tile("pink", "green"),
Cosigned = formatter("span",
style = x ~ style(
"border-radius" = "4px",
"padding-right" = "4px",
"background-color" = sapply(x,bg.picker)),
x ~ sprintf("%.2f (rank: %02d)", x, rank(-x)))
))| Variable | N | Mean | SD | Min | 25% | Median | 75% | Max | Kurtosis | Skewness |
|---|---|---|---|---|---|---|---|---|---|---|
| Head | 76 | 5.871 | 0.954 | 2.000 | 5.611 | 6.000 | 6.477 | 7.000 | 6.364 | -1.541 |
| Heart | 76 | 6.108 | 0.841 | 2.833 | 5.792 | 6.167 | 6.833 | 7.000 | 5.610 | -1.405 |
| Hand | 76 | 6.020 | 0.935 | 1.929 | 5.768 | 6.078 | 6.714 | 7.000 | 7.280 | -1.784 |
| IWB | 76 | 4.931 | 0.864 | 1.889 | 4.556 | 5.000 | 5.667 | 6.222 | 4.256 | -1.048 |
ST <- as.data.frame(sumtable(dfFac[c(01:03)], out = 'return', title='Summary Statistics by Factor', digits = 3, fixed.digits = TRUE,
summ = list(
c('notNA(x)','mean(x)','sd(x)','min(x)', 'pctile(x)[25]', 'median(x)', 'pctile(x)[75]', 'max(x)', 'kurtosis(x)', 'skewness(x)')
),
summ.names = list(
c('N','Mean','SD','Min', '25%', 'Median', '75%', 'Max', 'Kurtosis', 'Skewness')
)
))
formattable(ST, caption = "Summary Statistics by Factor - ILS", align = c("l", "c", "c", "c", "c", "c", "c", "c", "c", "c", "c"), list(
Mean = color_tile("pink", "green"),
Cosigned = formatter("span",
style = x ~ style(
"border-radius" = "4px",
"padding-right" = "4px",
"background-color" = sapply(x,bg.picker)),
x ~ sprintf("%.2f (rank: %02d)", x, rank(-x)))
))| Variable | N | Mean | SD | Min | 25% | Median | 75% | Max | Kurtosis | Skewness |
|---|---|---|---|---|---|---|---|---|---|---|
| Head | 76 | 5.871 | 0.954 | 2.000 | 5.611 | 6.000 | 6.477 | 7 | 6.364 | -1.541 |
| Heart | 76 | 6.108 | 0.841 | 2.833 | 5.792 | 6.167 | 6.833 | 7 | 5.610 | -1.405 |
| Hand | 76 | 6.020 | 0.935 | 1.929 | 5.768 | 6.078 | 6.714 | 7 | 7.280 | -1.784 |
2.2 Calculate Cronbach’s Alpha
Cronbach’s Alpha is an indicator for scale reliability. Raw alpha is sensitive to differences in the item variances. Standardized alpha is based upon the correlations rather than the covariances. Standardized alpha is based on the assumption that all of the items have equal variances, which is often false in practice. We use raw alpha to evaluate the scales. A level of 0.7 and above is acceptable, whereas 0.8 should be achieved in research. When making important data driven decisions, 0.9 marks a minimum. If Guttman’s Lambda 6 (G6) is higher than Alpha, factor shows unequal item loadings.
# Loading necessary packages
if(! "psych" %in% installed.packages()) { install.packages("psych", dependencies = TRUE) }
library(psych)
# Cronbach's Alpha
cAlpha <- psych::alpha(x = dfValFull[c(1,2)])
alphaDT <- data.table(variable = "Envision Change", id = "B01", cAlpha$total)
cAlpha <- psych::alpha(x = dfValFull[c(3,4,5)])
alphaDT <- rbind(alphaDT, data.table(variable = "Promote Change", id = "B02", cAlpha$total))
cAlpha <- psych::alpha(x = dfValFull[c(7,8,9)])
alphaDT <- rbind(alphaDT, data.table(variable = "Manage Change", id = "B03", cAlpha$total))
cAlpha <- psych::alpha(x = dfValFull[c(10,11,12)])
alphaDT <- rbind(alphaDT, data.table(variable = "Drive Innovation", id = "B04", cAlpha$total))
cAlpha <- psych::alpha(x = dfValFull[c(14,15,16)])
alphaDT <- rbind(alphaDT, data.table(variable = "Build Relationship", id = "B05", cAlpha$total))
cAlpha <- psych::alpha(x = dfValFull[c(13,17,18)])
alphaDT <- rbind(alphaDT, data.table(variable = "Support Others", id = "B06", cAlpha$total))
cAlpha <- psych::alpha(x = dfValFull[c(20,21,22,23)])
alphaDT <- rbind(alphaDT, data.table(variable = "Make Decision", id = "B07", cAlpha$total))
cAlpha <- psych::alpha(x = dfValFull[c(24,25,26)])
alphaDT <- rbind(alphaDT, data.table(variable = "Make Things Happen", id = "B08", cAlpha$total))
cAlpha <- psych::alpha(x = dfValFull[c(27,28)])
alphaDT <- rbind(alphaDT, data.table(variable = "Solve Problems Creatively", id = "B09", cAlpha$total))
cAlpha <- psych::alpha(x = dfValFull[c(30,31)])
alphaDT <- rbind(alphaDT, data.table(variable = "Take Responsibility", id = "B10", cAlpha$total))
cAlpha <- psych::alpha(x = dfValFull[c(32,33,34)])
alphaDT <- rbind(alphaDT, data.table(variable = "Demonstrate Team Leadership", id = "B11", cAlpha$total))
cAlpha <- psych::alpha(x = dfValFull[c(01:05,07:12)])
alphaDT <- rbind(alphaDT, data.table(variable = "Head", id = "Hed", cAlpha$total))
cAlpha <- psych::alpha(x = dfValFull[c(13:18)])
alphaDT <- rbind(alphaDT, data.table(variable = "Heart", id = "Hrt", cAlpha$total))
cAlpha <- psych::alpha(x = dfValFull[c(20:28,30:34)])
alphaDT <- rbind(alphaDT, data.table(variable = "Hand", id = "Hnd", cAlpha$total))
cAlpha <- psych::alpha(x = dfVal)
alphaDT <- rbind(alphaDT, data.table(variable = "ILS", id = "ILS", cAlpha$total))
cAlpha <- psych::alpha(x = dfValFull[c(35:43)])
alphaDT <- rbind(alphaDT, data.table(variable = "Innovative Work Behaviour", id = "IWB", cAlpha$total))
alphaDT$LCL <- alphaDT$raw_alpha - 2 * alphaDT$ase
alphaDT$UCL <- alphaDT$raw_alpha + 2 * alphaDT$ase
# alphaDT$StdAlpha <- alphaDT$std.alpha
# Remove columns
alphaDT <- alphaDT[,-c("S/N", "std.alpha", "average_r", "median_r", "ase")]
# Rename columns
setnames(alphaDT, "variable", "Variable")
setnames(alphaDT, "id", "ID")
setnames(alphaDT, "raw_alpha", "Raw Alpha")
setnames(alphaDT, "G6(smc)", "G6")
setnames(alphaDT, "mean", "Mean")
setnames(alphaDT, "sd", "SD")
# setnames(alphaDT, "StdAlpha", "Std Alpha")
options("digits" = 3)
# Show Cronbach's alpha table
improvement_formatter <- formatter("span", font.weight = "bold")
alphaDT <- alphaDT %>% mutate(across(`Raw Alpha`:UCL, ~ formattable::comma(., digits = 3)))
formattable(alphaDT,
align = c("l","c","c","c","c","c","c","c"),
list(
`Indicator Name` = formatter("span", style = ~ style(color = "grey",font.weight = "bold")),
`Raw Alpha` = formattable::color_tile("pink","lightgreen"),
`Improvement` = improvement_formatter)
)| Variable | ID | Raw Alpha | G6 | Mean | SD | LCL | UCL |
|---|---|---|---|---|---|---|---|
| Envision Change | B01 | 0.885 | 0.798 | 5.889 | 1.057 | 0.833 | 0.937 |
| Promote Change | B02 | 0.902 | 0.864 | 5.910 | 1.001 | 0.863 | 0.941 |
| Manage Change | B03 | 0.909 | 0.872 | 5.861 | 0.973 | 0.874 | 0.945 |
| Drive Innovation | B04 | 0.916 | 0.882 | 5.830 | 0.973 | 0.882 | 0.949 |
| Build Relationship | B05 | 0.826 | 0.779 | 6.202 | 0.768 | 0.761 | 0.892 |
| Support Others | B06 | 0.903 | 0.875 | 6.013 | 1.007 | 0.865 | 0.942 |
| Make Decision | B07 | 0.928 | 0.914 | 5.994 | 0.929 | 0.901 | 0.955 |
| Make Things Happen | B08 | 0.892 | 0.846 | 6.008 | 0.983 | 0.849 | 0.935 |
| Solve Problems Creatively | B09 | 0.904 | 0.825 | 5.940 | 1.036 | 0.860 | 0.948 |
| Take Responsibility | B10 | 0.915 | 0.848 | 6.195 | 0.937 | 0.877 | 0.953 |
| Demonstrate Team Leadership | B11 | 0.899 | 0.872 | 6.004 | 1.007 | 0.858 | 0.940 |
| Head | Hed | 0.972 | 0.975 | 5.871 | 0.954 | 0.963 | 0.982 |
| Heart | Hrt | 0.916 | 0.916 | 6.108 | 0.841 | 0.889 | 0.944 |
| Hand | Hnd | 0.979 | 0.984 | 6.020 | 0.935 | 0.971 | 0.986 |
| ILS | ILS | 0.989 | 0.996 | 5.747 | 0.883 | 0.985 | 0.992 |
| Innovative Work Behaviour | IWB | 0.930 | 0.930 | 4.931 | 0.864 | 0.906 | 0.954 |
# Write Cronbach's Alpha
setwd("~/AB PRIVATE/01 Amy/AB Amy PhD/Part 3/Data/Study3")
write.csv(alphaDT, file = paste(today, "CronbachAlpha.csv"))3 Showing Graphs of Data
3.1 Plot Histograms of all Variables
# Setting working Directory
setwd("~/AB PRIVATE/01 Amy/AB Amy PhD/Part 3/Data/Study3")
# Prepare PDF
if (makePDF) {
pdf(paste(today, "Hist.pdf"), width = 25, height = 16)
}
par(mar=c(7, 1, 7, 1))
par(oma=c(1, 1, 1, 1))
par(mfrow=c(2, 2), mai=c(2, 1, 2, 1))
hist(dfFac$Head, prob = T, xlim = c(1, 7), col = "lightblue", xlab= "", ylab="", cex.lab = 2.5, cex.axis = 2.5, cex.main = 3.0, main = "Histogram of Head", breaks = 10)
hist(dfFac$Heart, prob = T, xlim = c(1, 7), col = "#ffcc00", xlab= "", ylab="", cex.lab = 2.5, cex.axis = 2.5, cex.main = 3.0, main = "Histogram of Heart", breaks = 10)
hist(dfFac$Hand, prob = T, xlim = c(1, 7), col = "lightgreen", xlab= "", ylab="", cex.lab = 2.5, cex.axis = 2.5, cex.main = 3.0, main = "Histogram of Hand", breaks = 10)
hist(dfFac$IWB, prob = T, xlim = c(1, 7), col = "pink", xlab= "", ylab="", cex.lab = 2.5, cex.axis = 2.5, cex.main = 3.0, main = "Histogram of IWB", breaks = 10)
if (makePDF) {
dev.off()
}3.2 Show Error Plot of Items per Factor
Error plots give an idea of potential misfitting items (questions/statements) per factor (variable.)
# Setting working Directory
setwd("~/AB PRIVATE/01 Amy/AB Amy PhD/Part 3/Data/Study3")
# Prepare PDF
if (makePDF) {
pdf(paste(today, "Error.pdf"), width = 25, height = 25)
}
par(mar=c(2, 1, 2, 1))
par(oma=c(1, 1, 1, 1))
par(mfrow=c(2, 2))
layout.matrix <- matrix(c(0, 2, 3, 1), nrow = 2, ncol = 2)
# Create mean scores and confidence intervals
error.dots(dfHead, eyes = TRUE, sort = FALSE, main = "Head - Mean Confidence Interval", xlim = c(1, 7), lcolor = "blue", cex = 1.5, cex.main = 1, pch = 19, color = "blue")
error.dots(dfHeart, eyes = TRUE, sort = FALSE, main = "Heart - Mean Confidence Interval", xlim = c(1, 7), lcolor = "darkgreen", cex = 1.5, cex.main = 1, pch = 19, color = "#CC6633")
error.dots(dfHand, eyes = TRUE, sort = FALSE, main = "Hand - Mean Confidence Interval", xlim = c(1, 7), lcolor = "magenta", cex = 1.5, cex.main = 1, pch = 19, color = "darkgreen")
error.dots(dfIWB, eyes = TRUE, sort = FALSE, main = "IWB - Mean Confidence Interval", xlim = c(1, 7), lcolor = "red", cex = 1.5, cex.main = 1, pch = 19, color = "red")
if (makePDF) {
dev.off()
}3.3 Show Item List
# Make Item Data Table
improvement_formatter <- formatter("span", font.weight = "bold")
formattable(dfItems[1:31,], caption = "List of Items at ILS",
align = c("c","l","l", "c"),
list(
`Indicator Name` = formatter("span", style = ~ style(color = "grey",font.weight = "bold")),
`Mean` = formattable::color_tile("pink","lightgreen"),
`Improvement` = improvement_formatter)
)| Item | Behavior | Statement |
|---|---|---|
| SN01 | Protected | Protected |
formattable(dfItems[32:40,], caption = "List of Items at IWB",
align = c("c","l","l", "c"),
list(
`Indicator Name` = formatter("span", style = ~ style(color = "grey",font.weight = "bold")),
`Mean` = formattable::color_tile("pink","lightgreen"),
`Improvement` = improvement_formatter)
)| Item | Behavior | Statement |
|---|---|---|
| IWB01 | Protected | Protected |
3.4 Plot Correlation Matrix of Items
dfMatrix <- cor(dfVal)
corrplot.mixed(dfMatrix, lower = 'number', upper = 'pie', number.cex = 0.7, cl.cex = 1.0, tl.cex = 0.5)
# Write Correlation Matrix
setwd("~/AB PRIVATE/01 Amy/AB Amy PhD/Part 3/Data/Study3")
write.csv(dfMatrix, file = paste(today, "SNCorrelation.csv"))
dev.off()## null device
## 13.5 Plot Correlation Matrix of Behaviours
# Preparing Correlation Plot
Mat <- cor(dfBeh)
Res <- cor.mtest(dfBeh, conf.level = .95)
corrplot.mixed(Mat, lower.col = "black", number.cex = 1.0, upper = "pie", tl.col = "blue", tl.cex = 1.5, p.mat = Res$p, insig = "p-value", cl.ratio = 0.2, cl.align = "r", cl.lim = c(0, 1), cl.cex = 1.0, number.digits = 3)
corr.test(dfBeh, y = NULL, use = "pairwise", method="pearson", adjust="holm", alpha=.05, ci=TRUE, minlength=5, normal=TRUE)## Call:corr.test(x = dfBeh, y = NULL, use = "pairwise", method = "pearson",
## adjust = "holm", alpha = 0.05, ci = TRUE, minlength = 5,
## normal = TRUE)
## Correlation matrix
## B01 B02 B03 B04 B05 B06 B07 B08 B09 B10 B11 IWB
## B01 1.00 0.89 0.91 0.83 0.65 0.83 0.85 0.84 0.84 0.80 0.86 0.85
## B02 0.89 1.00 0.92 0.88 0.69 0.85 0.87 0.88 0.86 0.85 0.88 0.89
## B03 0.91 0.92 1.00 0.90 0.74 0.84 0.88 0.85 0.88 0.85 0.91 0.90
## B04 0.83 0.88 0.90 1.00 0.78 0.85 0.92 0.88 0.87 0.84 0.87 0.90
## B05 0.65 0.69 0.74 0.78 1.00 0.79 0.77 0.76 0.78 0.77 0.78 0.76
## B06 0.83 0.85 0.84 0.85 0.79 1.00 0.89 0.86 0.87 0.88 0.91 0.87
## B07 0.85 0.87 0.88 0.92 0.77 0.89 1.00 0.91 0.88 0.92 0.92 0.89
## B08 0.84 0.88 0.85 0.88 0.76 0.86 0.91 1.00 0.86 0.90 0.89 0.88
## B09 0.84 0.86 0.88 0.87 0.78 0.87 0.88 0.86 1.00 0.87 0.91 0.89
## B10 0.80 0.85 0.85 0.84 0.77 0.88 0.92 0.90 0.87 1.00 0.90 0.86
## B11 0.86 0.88 0.91 0.87 0.78 0.91 0.92 0.89 0.91 0.90 1.00 0.89
## IWB 0.85 0.89 0.90 0.90 0.76 0.87 0.89 0.88 0.89 0.86 0.89 1.00
## Sample Size
## [1] 76
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## B01 B02 B03 B04 B05 B06 B07 B08 B09 B10 B11 IWB
## B01 0 0 0 0 0 0 0 0 0 0 0 0
## B02 0 0 0 0 0 0 0 0 0 0 0 0
## B03 0 0 0 0 0 0 0 0 0 0 0 0
## B04 0 0 0 0 0 0 0 0 0 0 0 0
## B05 0 0 0 0 0 0 0 0 0 0 0 0
## B06 0 0 0 0 0 0 0 0 0 0 0 0
## B07 0 0 0 0 0 0 0 0 0 0 0 0
## B08 0 0 0 0 0 0 0 0 0 0 0 0
## B09 0 0 0 0 0 0 0 0 0 0 0 0
## B10 0 0 0 0 0 0 0 0 0 0 0 0
## B11 0 0 0 0 0 0 0 0 0 0 0 0
## IWB 0 0 0 0 0 0 0 0 0 0 0 0
##
## To see confidence intervals of the correlations, print with the short=FALSE option# Write Correlation Matrix
setwd("~/AB PRIVATE/01 Amy/AB Amy PhD/Part 3/Data/Study3")
write.csv(Mat, file = paste(today, "BehCorrelation.csv"))3.6 Plot Correlation Matrix of Behaviours with p-value
3.7 Plot Correlation Matrix of Factors
# Preparing Correlation Plot
Mat <- cor(dfFac)
Res <- cor.mtest(dfFac, conf.level = .95)
corrplot.mixed(Mat, lower.col = "black", number.cex = 1.0, upper = "pie", tl.col = "blue", tl.cex = 1.5, p.mat = Res$p, insig = "p-value", cl.ratio = 0.2, cl.align = "r", cl.lim = c(0, 1), cl.cex = 1.0, number.digits = 3)
corr.test(dfFac, y = NULL, use = "pairwise", method="pearson", adjust="holm", alpha=.05, ci=TRUE, minlength=5, normal=TRUE)## Call:corr.test(x = dfFac, y = NULL, use = "pairwise", method = "pearson",
## adjust = "holm", alpha = 0.05, ci = TRUE, minlength = 5,
## normal = TRUE)
## Correlation matrix
## Head Heart Hand IWB
## Head 1.00 0.87 0.95 0.93
## Heart 0.87 1.00 0.92 0.87
## Hand 0.95 0.92 1.00 0.92
## IWB 0.93 0.87 0.92 1.00
## Sample Size
## [1] 76
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## Head Heart Hand IWB
## Head 0 0 0 0
## Heart 0 0 0 0
## Hand 0 0 0 0
## IWB 0 0 0 0
##
## To see confidence intervals of the correlations, print with the short=FALSE option# Write Correlation Matrix
setwd("~/AB PRIVATE/01 Amy/AB Amy PhD/Part 3/Data/Study3")
write.csv(Mat, file = paste(today, "FacCorrelation.csv")) 3.8 Plot Correlation Matrix of Factor Items
# Setting working Directory
setwd("~/AB PRIVATE/01 Amy/AB Amy PhD/Part 3/Data/Study3")
# Prepare PDF
if (makePDF) {
pdf(paste(today, "CorrFactor.pdf"), width = 25, height = 16)
}
par(mar=c(7, 1, 7, 1))
par(oma=c(1, 1, 1, 1))
Mat <- cor(dfHead)
Res <- cor.mtest(dfHead, conf.level = .95)
corrplot.mixed(Mat, lower.col = "black", number.cex = 2.0, upper = "pie", tl.col = "blue", tl.cex = 2.0, p.mat = Res$p, insig = "p-value", cl.ratio = 0.2, cl.align = "r", cl.lim = c(0, 1), cl.cex = 2.0, cex.main = 3, main = "Correlation of Head Items", mar = c(2,0,2,0), number.digits = 3 )
Mat <- cor(dfHeart)
Res <- cor.mtest(dfHeart, conf.level = .95)
corrplot.mixed(Mat, lower.col = "black", number.cex = 2.0, upper = "pie", tl.col = "blue", tl.cex = 2.0, p.mat = Res$p, insig = "p-value", cl.ratio = 0.2, cl.align = "r", cl.lim = c(0, 1), cl.cex = 2.0, cex.main = 3, main = "Correlation of Heart Items", mar = c(2,0,2,0), number.digits = 3 )
Mat <- cor(dfHand)
Res <- cor.mtest(dfHand, conf.level = .95)
corrplot.mixed(Mat, lower.col = "black", number.cex = 2.0, upper = "pie", tl.col = "blue", tl.cex = 2.0, p.mat = Res$p, insig = "p-value", cl.ratio = 0.2, cl.align = "r", cl.lim = c(0, 1), cl.cex = 2.0, cex.main = 3, main = "Correlation of Hand Items", mar = c(2,0,2,0), number.digits = 3 )
Mat <- cor(dfIWB)
Res <- cor.mtest(dfIWB, conf.level = .95)
corrplot.mixed(Mat, lower.col = "black", number.cex = 2.0, upper = "pie", tl.col = "blue", tl.cex = 2.0, p.mat = Res$p, insig = "p-value", cl.ratio = 0.2, cl.align = "r", cl.lim = c(0, 1), cl.cex = 2.0, cex.main = 3, main = "Correlation of IWB Items", mar = c(2,0,2,0), number.digits = 3)
if (makePDF) {
dev.off()
}4 Testing Whether ILS Scale of Study 2 is Confirmed in Study 3 - 287 Raters
4.1 Calculate KMO
Measured by the Kaiser-Meyer-Olkin (KMO) statistics, sampling adequacy predicts if data are likely to factor well, based on correlation and partial correlation. If it´s value is lower then 0.6 then you should inspect those variables to decide which one should not take part of the factor analysis. To do so drop the indicator variables with the lowest individual KMO statistic values, until KMO overall rises above 0.60.
matrix <- cor(dfValNoIWB)
# Printing output
cat("Factorability of all data: ", round(KMO(matrix)$MSA, 4), "\n\nDetails: ")## Factorability of all data: 0.978
##
## Details:KMO(r = cor(dfValNoIWB))## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = cor(dfValNoIWB))
## Overall MSA = 0.98
## MSA for each item =
## SN01 SN02 SN03 SN04 SN05 SN07 SN08 SN09 SN10 SN11 SN12 SN13 SN14 SN15 SN16 SN17
## 0.99 0.97 0.98 0.97 0.98 0.98 0.98 0.98 0.97 0.98 0.98 0.97 0.96 0.96 0.97 0.98
## SN18 SN20 SN21 SN22 SN23 SN24 SN25 SN26 SN27 SN28 SN30 SN31 SN32 SN33 SN34
## 0.97 0.98 0.98 0.99 0.99 0.99 0.98 0.98 0.98 0.99 0.98 0.97 0.98 0.98 0.98cat("\n\nBartlet Test for homogenity of variance:\n")##
##
## Bartlet Test for homogenity of variance:cat("Chi Square: ", cortest.bartlett(matrix)$chisq, "\n")## Chi Square: 2758cat("P value: ", cortest.bartlett(matrix)$p.value, "\n")## P value: 3.93e-321cat("Degree of freedom: ", cortest.bartlett(matrix)$df, "\n\n")## Degree of freedom: 465cat("Determinant of matrix: ", det(cor(dfValNoIWB)), "\n")## Determinant of matrix: 0.0000000000000231rm(matrix, Res, layout.matrix)
# cat("KMO: ", format(KMO, nsmall = 4), ".\n")
# cat("Sphericity: ", format(Sphericity, nsmall = 4), ".\n")4.2 Principal component analysis - 287 Raters
The number of components is also the number of variables.
Proportion of variance: If it equals to 0.85 then it explains 85% of the variance. Cumulative Proportion: Cumulates the proportion of the previous components adding up until 1. Choose the number of components (factors) with eigenvalues equal or higher then 1 using the Principal Component function.
# Loading necessary packages
if(! "lavaan" %in% installed.packages()) {install.packages("lavaan", dependencies = TRUE) }
library(lavaan)
pca = princomp(dfValNoIWB, scores = TRUE, cor = TRUE)
summary(pca)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8
## Standard deviation 4.442 1.2012 0.9426 0.7943 0.7768 0.7332 0.7078 0.6993
## Proportion of Variance 0.636 0.0465 0.0287 0.0204 0.0195 0.0173 0.0162 0.0158
## Cumulative Proportion 0.636 0.6829 0.7116 0.7319 0.7514 0.7687 0.7849 0.8007
## Comp.9 Comp.10 Comp.11 Comp.12 Comp.13 Comp.14 Comp.15
## Standard deviation 0.6708 0.6572 0.6319 0.6247 0.6015 0.5887 0.5739
## Proportion of Variance 0.0145 0.0139 0.0129 0.0126 0.0117 0.0112 0.0106
## Cumulative Proportion 0.8152 0.8291 0.8420 0.8546 0.8663 0.8774 0.8881
## Comp.16 Comp.17 Comp.18 Comp.19 Comp.20 Comp.21 Comp.22
## Standard deviation 0.54814 0.53249 0.52980 0.51737 0.50781 0.49570 0.48245
## Proportion of Variance 0.00969 0.00915 0.00905 0.00863 0.00832 0.00793 0.00751
## Cumulative Proportion 0.89777 0.90691 0.91597 0.92460 0.93292 0.94085 0.94835
## Comp.23 Comp.24 Comp.25 Comp.26 Comp.27 Comp.28 Comp.29
## Standard deviation 0.47078 0.46294 0.45135 0.44405 0.41584 0.41376 0.38365
## Proportion of Variance 0.00715 0.00691 0.00657 0.00636 0.00558 0.00552 0.00475
## Cumulative Proportion 0.95550 0.96242 0.96899 0.97535 0.98093 0.98645 0.99120
## Comp.30 Comp.31
## Standard deviation 0.37795 0.36056
## Proportion of Variance 0.00461 0.00419
## Cumulative Proportion 0.99581 1.00000# pca$loadings4.3 Confirmatory factor analysis - 287 Raters
# Loading necessary packages
if(! "lavaan" %in% installed.packages()) {install.packages("lavaan", dependencies = TRUE) }
library(lavaan)
# Build model
Model01 <- '
# latent variables
Head =~ SN01 + SN02 + SN03 + SN04 + SN05 + SN07 + SN08 + SN09 + SN10 + SN11 + SN12
Heart =~ SN13 + SN14 + SN15 + SN16 + SN17 + SN18
Hand =~ SN20 + SN21 + SN22 + SN23 + SN24 + SN25 + SN26 + SN27 + SN28 + SN30 + SN31 + SN32 + SN33 + SN34
'
# Run CFA
CFA01 <- cfa(Model01, data = dfValNoIWB)
summary(CFA01, fit.measures = TRUE, standardized = TRUE)## lavaan 0.6-12 ended normally after 66 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 65
##
## Number of observations 287
##
## Model Test User Model:
##
## Test statistic 985.789
## Degrees of freedom 431
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 9011.304
## Degrees of freedom 465
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.935
## Tucker-Lewis Index (TLI) 0.930
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -8425.474
## Loglikelihood unrestricted model (H1) -7932.580
##
## Akaike (AIC) 16980.949
## Bayesian (BIC) 17218.815
## Sample-size adjusted Bayesian (BIC) 17012.693
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.067
## 90 Percent confidence interval - lower 0.061
## 90 Percent confidence interval - upper 0.072
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.039
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Head =~
## SN01 1.000 0.729 0.780
## SN02 1.222 0.076 16.094 0.000 0.891 0.839
## SN03 1.109 0.072 15.443 0.000 0.808 0.813
## SN04 1.279 0.080 15.913 0.000 0.932 0.831
## SN05 1.053 0.069 15.182 0.000 0.767 0.802
## SN07 1.201 0.074 16.164 0.000 0.876 0.841
## SN08 1.152 0.071 16.181 0.000 0.840 0.842
## SN09 1.063 0.070 15.162 0.000 0.775 0.801
## SN10 1.192 0.073 16.365 0.000 0.869 0.849
## SN11 1.173 0.073 16.122 0.000 0.855 0.840
## SN12 0.981 0.068 14.509 0.000 0.715 0.774
## Heart =~
## SN13 1.000 0.713 0.788
## SN14 0.967 0.074 13.112 0.000 0.690 0.719
## SN15 1.084 0.072 15.035 0.000 0.773 0.801
## SN16 1.203 0.075 16.040 0.000 0.858 0.841
## SN17 1.163 0.070 16.590 0.000 0.829 0.863
## SN18 1.098 0.077 14.319 0.000 0.783 0.771
## Hand =~
## SN20 1.000 0.820 0.815
## SN21 0.926 0.054 17.143 0.000 0.760 0.832
## SN22 1.007 0.057 17.725 0.000 0.826 0.851
## SN23 0.851 0.055 15.611 0.000 0.698 0.781
## SN24 0.999 0.059 16.823 0.000 0.820 0.822
## SN25 1.011 0.061 16.662 0.000 0.829 0.817
## SN26 0.955 0.059 16.201 0.000 0.783 0.801
## SN27 0.967 0.057 17.075 0.000 0.793 0.830
## SN28 1.090 0.060 18.179 0.000 0.894 0.865
## SN30 0.805 0.050 16.080 0.000 0.661 0.797
## SN31 0.857 0.055 15.555 0.000 0.703 0.779
## SN32 1.010 0.059 17.055 0.000 0.828 0.830
## SN33 1.006 0.065 15.510 0.000 0.825 0.777
## SN34 0.986 0.059 16.622 0.000 0.809 0.815
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Head ~~
## Heart 0.430 0.050 8.638 0.000 0.828 0.828
## Hand 0.566 0.061 9.307 0.000 0.947 0.947
## Heart ~~
## Hand 0.528 0.058 9.142 0.000 0.902 0.902
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SN01 0.342 0.030 11.346 0.000 0.342 0.392
## .SN02 0.335 0.030 11.011 0.000 0.335 0.297
## .SN03 0.336 0.030 11.185 0.000 0.336 0.340
## .SN04 0.388 0.035 11.064 0.000 0.388 0.309
## .SN05 0.327 0.029 11.243 0.000 0.327 0.357
## .SN07 0.317 0.029 10.989 0.000 0.317 0.292
## .SN08 0.290 0.026 10.983 0.000 0.290 0.291
## .SN09 0.335 0.030 11.248 0.000 0.335 0.358
## .SN10 0.292 0.027 10.922 0.000 0.292 0.279
## .SN11 0.306 0.028 11.002 0.000 0.306 0.295
## .SN12 0.342 0.030 11.370 0.000 0.342 0.401
## .SN13 0.310 0.029 10.650 0.000 0.310 0.379
## .SN14 0.445 0.040 11.117 0.000 0.445 0.483
## .SN15 0.334 0.032 10.529 0.000 0.334 0.359
## .SN16 0.304 0.030 10.008 0.000 0.304 0.292
## .SN17 0.236 0.025 9.605 0.000 0.236 0.256
## .SN18 0.418 0.039 10.793 0.000 0.418 0.405
## .SN20 0.340 0.030 11.366 0.000 0.340 0.336
## .SN21 0.256 0.023 11.279 0.000 0.256 0.307
## .SN22 0.260 0.023 11.166 0.000 0.260 0.276
## .SN23 0.311 0.027 11.495 0.000 0.311 0.390
## .SN24 0.322 0.028 11.333 0.000 0.322 0.324
## .SN25 0.343 0.030 11.358 0.000 0.343 0.333
## .SN26 0.342 0.030 11.423 0.000 0.342 0.358
## .SN27 0.284 0.025 11.291 0.000 0.284 0.311
## .SN28 0.270 0.024 11.059 0.000 0.270 0.253
## .SN30 0.250 0.022 11.439 0.000 0.250 0.365
## .SN31 0.320 0.028 11.501 0.000 0.320 0.393
## .SN32 0.311 0.028 11.295 0.000 0.311 0.312
## .SN33 0.446 0.039 11.506 0.000 0.446 0.396
## .SN34 0.330 0.029 11.364 0.000 0.330 0.335
## Head 0.531 0.068 7.837 0.000 1.000 1.000
## Heart 0.508 0.065 7.869 0.000 1.000 1.000
## Hand 0.673 0.080 8.388 0.000 1.000 1.000# pca$loadings4.4 Factor Analysis - 287 Raters
# Factor analysis
fa = factanal(dfValNoIWB, factor = 3, rotation = "Promax", scores = "regression")
fa##
## Call:
## factanal(x = dfValNoIWB, factors = 3, scores = "regression", rotation = "Promax")
##
## Uniquenesses:
## SN01 SN02 SN03 SN04 SN05 SN07 SN08 SN09 SN10 SN11 SN12 SN13 SN14
## 0.374 0.310 0.353 0.275 0.358 0.304 0.263 0.367 0.248 0.263 0.377 0.393 0.315
## SN15 SN16 SN17 SN18 SN20 SN21 SN22 SN23 SN24 SN25 SN26 SN27 SN28
## 0.301 0.250 0.282 0.402 0.336 0.314 0.280 0.318 0.318 0.323 0.351 0.294 0.258
## SN30 SN31 SN32 SN33 SN34
## 0.290 0.304 0.317 0.395 0.329
##
## Loadings:
## Factor1 Factor2 Factor3
## SN01 0.393 0.490
## SN02 0.768
## SN03 0.643 0.226
## SN04 0.908 -0.118
## SN05 0.475 0.421
## SN07 0.686 0.188
## SN08 0.907
## SN09 0.727
## SN10 0.865 -0.167 0.201
## SN11 0.944 -0.111
## SN12 0.430 0.214 0.221
## SN13 0.469 0.389
## SN14 0.864
## SN15 0.154 0.656
## SN16 0.208 0.684
## SN17 0.643 0.310
## SN18 0.204 0.450 0.183
## SN20 0.573 0.287
## SN21 0.267 0.528
## SN22 0.523 0.327
## SN23 0.822
## SN24 0.309 0.581
## SN25 0.370 0.571 -0.116
## SN26 0.241 0.596
## SN27 0.633 0.184
## SN28 0.500 0.328
## SN30 0.866
## SN31 -0.130 0.876
## SN32 0.333 0.515
## SN33 0.201 0.579
## SN34 0.517 0.379
##
## Factor1 Factor2 Factor3
## SS loadings 7.984 6.066 2.108
## Proportion Var 0.258 0.196 0.068
## Cumulative Var 0.258 0.453 0.521
##
## Factor Correlations:
## Factor1 Factor2 Factor3
## Factor1 1.000 -0.832 -0.642
## Factor2 -0.832 1.000 0.724
## Factor3 -0.642 0.724 1.000
##
## Test of the hypothesis that 3 factors are sufficient.
## The chi square statistic is 662 on 375 degrees of freedom.
## The p-value is 0.000000000000000003445 Testing Whether ILS Factors Influence IWB - 76 Raters
5.1 How to Evaluate SEM Output?
Chisq: The model Chi-squared assesses overall fit and the discrepancy between the sample and fitted covariance matrices. Its p-value should be > .05 (i.e., the hypothesis of a perfect fit cannot be rejected). However, it is quite sensitive to sample size. Commonly, Chisq/DF < 3 is used as criteria.
GFI/AGFI: The (Adjusted) Goodness of Fit is the proportion of variance accounted for by the estimated population covariance. Analogous to R2. The GFI and the AGFI should be > .95 and > .90, respectively.
NFI/NNFI/TLI: The (Non) Normed Fit Index. An NFI of 0.95, indicates the model of interest improves the fit by 95% relative to the null model. The NNFI (also called the Tucker Lewis index; TLI) is preferable for smaller samples. They should be > .90 (Byrne, 1994) or > .95 (Schumacker & Lomax, 2004). TLI > .90. TLI: < .85(poor); .85-.90 (mediocre); .90-.95 (acceptable); .95-.99 (close); 1.00 (perfect)
CFI: The Comparative Fit Index is a revised form of NFI. Not very sensitive to sample size (Fan, Thompson, & Wang, 1999). Compares the fit of a target model to the fit of an independent, or null, model. CFI: < .85(poor); .85-.90 (mediocre); .90-.95 (acceptable); .95-.99 (close); 1.00 (perfect)
RMSEA: The Root Mean Square Error of Approximation is a parsimony-adjusted index. Values closer to 0 represent a good fit. It should be < .08 or < .05. The p-value printed with it tests the hypothesis that RMSEA is less than or equal to .05 (a cutoff sometimes used for good fit), and thus should be not significant. RMSEA: > .10 (poor); .08-.10 (mediocre); .05-.08 (acceptable); .01-.05 (close); .00 (perfect)
RMR/SRMR: the (Standardized) Root Mean Square Residual represents the square-root of the difference between the residuals of the sample covariance matrix and the hypothesized model. As the RMR can be sometimes hard to interpret, better to use SRMR. SRMR: > .10 (poor); .08-.10 (mediocre); .05-.08 (acceptable); .01-.05 (close); .00 (perfect)
RFI: the Relative Fit Index, also known as RHO1, is not guaranteed to vary from 0 to 1. However, RFI close to 1 indicates a good fit.
IFI: the Incremental Fit Index (IFI) adjusts the Normed Fit Index (NFI) for sample size and degrees of freedom (Bollen’s, 1989). Over 0.90 is a good fit, but the index can exceed 1.
PNFI: the Parsimony-Adjusted Measures Index. There is no commonly agreed-upon cutoff value for an acceptable model for this index. Should be > 0.50.
To Report: chi-square, RMSEA, CFI, RMSEA and SRMR.
5.2 About Estimators
Commonly used estimation method Maximum Likelihood (ML) has been developed for continuous data following the normal-theory. This method is used to estimate all fit indices like RMSEA, CFI, and TLI. Since our data is generated using a 7-point Likert Scale, i.e. resulting in ordered discrete/categorical data, this method may not be the best to determine model fit (Yan Xia & Yanyun Yang, 2018).Therefore, methods based on Unweighted Least Squares (ULS) and Diagonally Weighted Least Squares (DWLS) based on polychoric correlation matrices have been considered in previous studies.
5.3 Build Model: Head -> Hand -> IWB with Heart as Mediator (MLR) - 76 Raters
# Loading necessary packages
if(! "lavaan" %in% installed.packages()) {install.packages("lavaan", dependencies = TRUE) }
library(lavaan)
Model05 <- '
# latent variables
IWB =~ IWB01 + IWB02 + IWB03 + IWB04 + IWB05 + IWB06 + IWB07 + IWB08 + IWB09
Head =~ SN01 + SN02 + SN03 + SN04 + SN05 + SN07 + SN08 + SN09 + SN10 + SN11 + SN12 + SN18
Heart =~ SN13 + SN14 + SN15 + SN16 + SN17
Hand =~ SN20 + SN21 + SN22 + SN23 + SN24 + SN25 + SN26 + SN27 + SN28 + SN30 + SN31 + SN32 + SN33 + SN34
# direct effect
IWB ~ a * Hand
Hand ~ d * Head
EffHnd := a
# mediator
Hand ~ b * Heart
Heart ~ c * Head
# covariances
IWB07 ~~ SN24
IWB03 ~~ SN16
SN02 ~~ SN30
SN04 ~~ SN31
SN05 ~~ SN30
SN12 ~~ SN21
SN13 ~~ SN20
SN15 ~~ SN24
SN16 ~~ SN20
SN21 ~~ SN34
SN21 ~~ SN22
SN24 ~~ SN28
# indirect effect
EffHrt := a * b
EffHed := a * (d + b * c)
'
# Calculate fit
Fit05 <- sem(Model05, data = dfVal, estimator = "MLR", likelihood = "wishart")
# Print results (fit indices, parameters, hypothesis tests)
summary(Fit05, fit.measures = TRUE, rsquare = TRUE)## lavaan 0.6-12 ended normally after 76 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 96
##
## Number of observations 76
##
## Model Test User Model:
## Standard Robust
## Test Statistic 1209.330 1233.195
## Degrees of freedom 724 724
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.981
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 4779.371 4858.433
## Degrees of freedom 780 780
## P-value 0.000 0.000
## Scaling correction factor 0.984
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.879 0.875
## Tucker-Lewis Index (TLI) 0.869 0.865
##
## Robust Comparative Fit Index (CFI) 0.876
## Robust Tucker-Lewis Index (TLI) 0.866
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2661.884 -2661.884
## Scaling correction factor 1.411
## for the MLR correction
## Loglikelihood unrestricted model (H1) -2049.157 -2049.157
## Scaling correction factor 1.031
## for the MLR correction
##
## Akaike (AIC) 5515.769 5515.769
## Bayesian (BIC) 5739.519 5739.519
## Sample-size adjusted Bayesian (BIC) 5436.920 5436.920
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.095 0.097
## 90 Percent confidence interval - lower 0.085 0.087
## 90 Percent confidence interval - upper 0.104 0.106
## P-value RMSEA <= 0.05 0.000 0.000
##
## Robust RMSEA 0.096
## 90 Percent confidence interval - lower 0.087
## 90 Percent confidence interval - upper 0.105
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.042 0.042
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## IWB =~
## IWB01 1.000
## IWB02 0.942 0.103 9.169 0.000
## IWB03 0.940 0.113 8.293 0.000
## IWB04 0.699 0.086 8.134 0.000
## IWB05 0.885 0.080 11.072 0.000
## IWB06 0.899 0.164 5.474 0.000
## IWB07 0.842 0.085 9.912 0.000
## IWB08 0.876 0.155 5.631 0.000
## IWB09 0.838 0.145 5.766 0.000
## Head =~
## SN01 1.000
## SN02 1.178 0.122 9.619 0.000
## SN03 0.998 0.112 8.892 0.000
## SN04 1.162 0.129 8.996 0.000
## SN05 1.031 0.149 6.911 0.000
## SN07 1.122 0.117 9.547 0.000
## SN08 1.013 0.106 9.588 0.000
## SN09 0.987 0.142 6.964 0.000
## SN10 1.085 0.113 9.582 0.000
## SN11 0.988 0.106 9.313 0.000
## SN12 0.971 0.112 8.696 0.000
## SN18 1.176 0.119 9.883 0.000
## Heart =~
## SN13 1.000
## SN14 0.450 0.192 2.350 0.019
## SN15 0.930 0.086 10.816 0.000
## SN16 0.908 0.090 10.134 0.000
## SN17 1.103 0.122 9.077 0.000
## Hand =~
## SN20 1.000
## SN21 0.924 0.086 10.678 0.000
## SN22 0.980 0.076 12.855 0.000
## SN23 0.876 0.098 8.967 0.000
## SN24 1.005 0.083 12.091 0.000
## SN25 1.011 0.109 9.279 0.000
## SN26 0.937 0.110 8.515 0.000
## SN27 1.094 0.103 10.658 0.000
## SN28 0.980 0.091 10.796 0.000
## SN30 0.881 0.089 9.947 0.000
## SN31 0.995 0.104 9.604 0.000
## SN32 1.031 0.077 13.372 0.000
## SN33 1.081 0.076 14.283 0.000
## SN34 0.981 0.082 11.957 0.000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## IWB ~
## Hand (a) 0.982 0.112 8.783 0.000
## Hand ~
## Head (d) 0.702 0.089 7.893 0.000
## Heart (b) 0.367 0.097 3.776 0.000
## Heart ~
## Head (c) 0.876 0.134 6.545 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .IWB07 ~~
## .SN24 0.168 0.063 2.669 0.008
## .IWB03 ~~
## .SN16 -0.127 0.035 -3.674 0.000
## .SN02 ~~
## .SN30 -0.088 0.032 -2.756 0.006
## .SN04 ~~
## .SN31 -0.097 0.049 -1.979 0.048
## .SN05 ~~
## .SN30 0.070 0.033 2.126 0.034
## .SN12 ~~
## .SN21 0.093 0.034 2.746 0.006
## .SN13 ~~
## .SN20 -0.105 0.040 -2.630 0.009
## .SN15 ~~
## .SN24 -0.083 0.033 -2.482 0.013
## .SN16 ~~
## .SN20 -0.104 0.039 -2.692 0.007
## .SN21 ~~
## .SN34 -0.070 0.031 -2.282 0.022
## .SN22 0.076 0.033 2.327 0.020
## .SN24 ~~
## .SN28 -0.096 0.032 -3.031 0.002
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .IWB01 0.292 0.045 6.495 0.000
## .IWB02 0.419 0.060 6.975 0.000
## .IWB03 0.428 0.063 6.794 0.000
## .IWB04 0.477 0.069 6.883 0.000
## .IWB05 0.362 0.053 6.819 0.000
## .IWB06 0.562 0.116 4.858 0.000
## .IWB07 0.564 0.097 5.844 0.000
## .IWB08 0.515 0.079 6.491 0.000
## .IWB09 0.603 0.095 6.345 0.000
## .SN01 0.314 0.084 3.749 0.000
## .SN02 0.241 0.066 3.670 0.000
## .SN03 0.285 0.067 4.276 0.000
## .SN04 0.283 0.070 4.021 0.000
## .SN05 0.296 0.070 4.224 0.000
## .SN07 0.248 0.067 3.695 0.000
## .SN08 0.259 0.043 6.084 0.000
## .SN09 0.230 0.061 3.746 0.000
## .SN10 0.256 0.051 5.060 0.000
## .SN11 0.256 0.041 6.196 0.000
## .SN12 0.316 0.076 4.179 0.000
## .SN18 0.365 0.082 4.483 0.000
## .SN13 0.259 0.050 5.160 0.000
## .SN14 0.406 0.089 4.547 0.000
## .SN15 0.260 0.061 4.289 0.000
## .SN16 0.243 0.050 4.827 0.000
## .SN17 0.175 0.047 3.714 0.000
## .SN20 0.302 0.057 5.249 0.000
## .SN21 0.216 0.039 5.559 0.000
## .SN22 0.212 0.039 5.470 0.000
## .SN23 0.278 0.077 3.626 0.000
## .SN24 0.300 0.067 4.496 0.000
## .SN25 0.329 0.060 5.462 0.000
## .SN26 0.338 0.079 4.298 0.000
## .SN27 0.169 0.042 3.997 0.000
## .SN28 0.289 0.062 4.629 0.000
## .SN30 0.173 0.035 4.980 0.000
## .SN31 0.183 0.047 3.926 0.000
## .SN32 0.462 0.188 2.463 0.014
## .SN33 0.198 0.050 3.989 0.000
## .SN34 0.194 0.039 5.027 0.000
## .IWB 0.043 0.028 1.521 0.128
## Head 0.803 0.275 2.914 0.004
## .Heart 0.167 0.047 3.546 0.000
## .Hand 0.014 0.010 1.463 0.143
##
## R-Square:
## Estimate
## IWB01 0.753
## IWB02 0.653
## IWB03 0.647
## IWB04 0.477
## IWB05 0.658
## IWB06 0.561
## IWB07 0.528
## IWB08 0.570
## IWB09 0.509
## SN01 0.719
## SN02 0.822
## SN03 0.737
## SN04 0.793
## SN05 0.742
## SN07 0.803
## SN08 0.761
## SN09 0.773
## SN10 0.787
## SN11 0.753
## SN12 0.705
## SN18 0.752
## SN13 0.752
## SN14 0.281
## SN15 0.722
## SN16 0.727
## SN17 0.845
## SN20 0.744
## SN21 0.776
## SN22 0.799
## SN23 0.708
## SN24 0.747
## SN25 0.732
## SN26 0.695
## SN27 0.862
## SN28 0.745
## SN30 0.798
## SN31 0.826
## SN32 0.669
## SN33 0.838
## SN34 0.813
## IWB 0.952
## Heart 0.787
## Hand 0.984
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|)
## EffHnd 0.982 0.112 8.783 0.000
## EffHrt 0.360 0.077 4.693 0.000
## EffHed 1.005 0.126 7.989 0.000modificationIndices(Fit05, minimum.value = 5)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 114 IWB =~ SN12 11.88 1.044 0.985 0.951 0.951
## 135 Head =~ IWB01 6.88 0.951 0.852 0.784 0.784
## 143 Head =~ IWB09 5.40 1.106 0.991 0.895 0.895
## 158 Head =~ SN30 6.27 -0.768 -0.688 -0.744 -0.744
## 168 Heart =~ IWB06 6.53 -0.846 -0.748 -0.661 -0.661
## 171 Heart =~ IWB09 5.47 -0.797 -0.705 -0.637 -0.637
## 182 Heart =~ SN12 20.59 0.800 0.708 0.684 0.684
## 193 Heart =~ SN30 6.88 0.467 0.414 0.448 0.448
## 217 Hand =~ SN12 16.00 1.698 1.591 1.536 1.536
## 222 Hand =~ SN16 5.12 -0.560 -0.524 -0.556 -0.556
## 270 IWB02 ~~ SN01 6.17 -0.109 -0.109 -0.300 -0.300
## 282 IWB02 ~~ SN13 6.12 0.099 0.099 0.300 0.300
## 331 IWB03 ~~ SN28 7.60 0.103 0.103 0.294 0.294
## 366 IWB04 ~~ SN27 7.80 0.095 0.095 0.335 0.335
## 410 IWB06 ~~ IWB09 5.96 0.170 0.170 0.292 0.292
## 424 IWB06 ~~ SN14 6.46 0.143 0.143 0.300 0.300
## 437 IWB06 ~~ SN30 6.51 -0.082 -0.082 -0.263 -0.263
## 450 IWB07 ~~ SN08 5.29 -0.095 -0.095 -0.247 -0.247
## 456 IWB07 ~~ SN13 6.12 -0.103 -0.103 -0.269 -0.269
## 466 IWB07 ~~ SN26 6.53 0.118 0.118 0.271 0.271
## 511 IWB09 ~~ SN07 5.22 0.107 0.107 0.276 0.276
## 512 IWB09 ~~ SN08 7.40 0.129 0.129 0.326 0.326
## 554 SN01 ~~ SN21 7.69 0.069 0.069 0.264 0.264
## 560 SN01 ~~ SN27 6.31 0.070 0.070 0.304 0.304
## 619 SN03 ~~ SN31 6.24 0.064 0.064 0.280 0.280
## 627 SN04 ~~ SN10 5.23 -0.071 -0.071 -0.263 -0.263
## 632 SN04 ~~ SN14 5.79 -0.090 -0.090 -0.266 -0.266
## 639 SN04 ~~ SN23 5.21 -0.071 -0.071 -0.254 -0.254
## 643 SN04 ~~ SN27 5.45 0.058 0.058 0.266 0.266
## 660 SN05 ~~ SN17 5.83 -0.067 -0.067 -0.296 -0.296
## 665 SN05 ~~ SN24 6.88 0.072 0.072 0.242 0.242
## 696 SN07 ~~ SN32 5.40 0.094 0.094 0.279 0.279
## 734 SN09 ~~ SN22 6.59 -0.061 -0.061 -0.278 -0.278
## 735 SN09 ~~ SN23 7.81 0.085 0.085 0.334 0.334
## 791 SN12 ~~ SN14 10.11 0.123 0.123 0.342 0.342
## 792 SN12 ~~ SN15 5.26 0.071 0.071 0.246 0.246
## 793 SN12 ~~ SN16 5.36 0.065 0.065 0.235 0.235
## 824 SN18 ~~ SN32 5.47 0.114 0.114 0.278 0.278
## 841 SN13 ~~ SN32 9.38 0.126 0.126 0.365 0.365
## 898 SN17 ~~ SN28 8.07 -0.080 -0.080 -0.354 -0.354
## 913 SN20 ~~ SN31 10.01 -0.075 -0.075 -0.318 -0.318
## 914 SN20 ~~ SN32 5.80 0.095 0.095 0.256 0.256
## 960 SN25 ~~ SN31 7.92 0.076 0.076 0.311 0.3115.4 Plot Model (MLR) - 76 Raters
# Loading necessary packages
if(! "semPlot" %in% installed.packages()) {install.packages("semPlot", dependencies = TRUE) }
library(semPlot)
# Setting working Directory
setwd("~/AB PRIVATE/01 Amy/AB Amy PhD/Part 3/Data/Study3")
# Prepare PDF for Model 05
if (makePDF) {
pdf(paste(today, "Model05.pdf"), width = 25, height = 25)
}
par(mar=c(7, 1, 7, 1))
par(oma=c(1, 1, 1, 1))
# Prepare fitmeasures
ParDF <- as.data.frame(do.call(cbind, Fit05@ParTable))
EffHed <- round(as.numeric(ParDF[ParDF$label == "EffHed", 14]), 4)
EffHrt <- round(as.numeric(ParDF[ParDF$label == "EffHrt", 14]), 4)
EffHnd <- round(as.numeric(ParDF[ParDF$label == "EffHnd", 14]), 4)
n <- Fit05@SampleStats@ntotal
fitMeas <- toString(c("ChiSq: ", round(as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "chisq"))), 4),
" - ChiSq-p: ", round(as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "pvalue"))), 4),
" - DF: ", gsub("[^0-9.]", "", fitMeasures(Fit05, "df")),
" - ChiSq/DF: ", round(as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "chisq")))/ as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "df"))), 4),
" - CFI: ", round(as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "cfi"))), 4),
" - TLI: ", round(as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "tli"))), 4),
" - RMSEA: ", round(as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "rmsea"))), 4),
" - SRMR: ", round(as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "srmr"))), 4),
" - n: ", n,
" - EffHed: ", EffHed,
" - EffHrt: ", EffHrt,
" - EffHnd: ", EffHnd
),
width = 255)
fitMeas <- gsub(",", "", fitMeas)
# Plot model
semPaths(Fit05, what = "eq", whatLabels = "stand", intercepts = FALSE, residuals = FALSE,
edge.label.cex = 0.7, edge.color = "blue", layout = "circle2", rotation = 3, curve = 1,
curvePivot = TRUE, mar = c(3,1,5,1), sizeLat = 7, sizeMan = 4, color = colorlist
)
title(main = "Model 5: Showing Head -> Hand -> IWB with Heart as Mediator\nEstimator: MLR - 76 Raters",
cex.main = 2.5, col.main = "darkblue", font.main = 3, sub = fitMeas, cex.sub = 1.4)
if (makePDF) {
dev.off()
}5.5 Build Model: Head -> Hand -> IWB with Heart as Mediator (WLSMV) - 76 Raters
# Loading necessary packages
if(! "lavaan" %in% installed.packages()) {install.packages("lavaan", dependencies = TRUE) }
library(lavaan)
Model05 <- '
# latent variables
IWB =~ IWB01 + IWB02 + IWB03 + IWB04 + IWB05 + IWB06 + IWB07 + IWB08 + IWB09
Head =~ SN01 + SN02 + SN03 + SN04 + SN05 + SN07 + SN08 + SN09 + SN10 + SN11 + SN12 + SN18
Heart =~ SN13 + SN14 + SN15 + SN16 + SN17
Hand =~ SN20 + SN21 + SN22 + SN23 + SN24 + SN25 + SN26 + SN27 + SN28 + SN30 + SN31 + SN32 + SN33 + SN34
# direct effect
IWB ~ a * Hand
Hand ~ d * Head
EffHnd := a
# mediator
Hand ~ b * Heart
Heart ~ c * Head
# covariances
IWB07 ~~ SN24
IWB03 ~~ SN16
SN02 ~~ SN30
SN04 ~~ SN31
SN05 ~~ SN30
SN12 ~~ SN21
SN13 ~~ SN20
SN15 ~~ SN24
SN16 ~~ SN20
SN21 ~~ SN34
SN21 ~~ SN22
SN24 ~~ SN28
# indirect effect
EffHrt := a * b
EffHed := a * (d + b * c)
'
# Calculate fit
Fit05 <- sem(Model05, data = dfVal, estimator = "WLSMV")
lavInspect(Fit05, "cov.lv")## IWB Head Heart Hand
## IWB 0.909
## Head 0.805 0.767
## Heart 0.767 0.683 0.799
## Hand 0.881 0.820 0.782 0.898# Print results (fit indices, parameters, hypothesis tests)
summary(Fit05, fit.measures = TRUE, rsquare = TRUE)## lavaan 0.6-12 ended normally after 75 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of model parameters 96
##
## Number of observations 76
##
## Model Test User Model:
## Standard Robust
## Test Statistic 38.551 747.705
## Degrees of freedom 724 724
## P-value (Chi-square) 1.000 0.263
## Scaling correction factor 0.241
## Shift parameter 587.674
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 9475.041 1189.609
## Degrees of freedom 780 780
## P-value 0.000 0.000
## Scaling correction factor 21.228
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000 0.942
## Tucker-Lewis Index (TLI) 1.085 0.938
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000 0.021
## 90 Percent confidence interval - lower 0.000 0.000
## 90 Percent confidence interval - upper 0.000 0.041
## P-value RMSEA <= 0.05 1.000 0.995
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.040 0.040
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## IWB =~
## IWB01 1.000
## IWB02 0.924 0.098 9.474 0.000
## IWB03 0.949 0.111 8.524 0.000
## IWB04 0.686 0.084 8.118 0.000
## IWB05 0.877 0.078 11.196 0.000
## IWB06 0.892 0.175 5.088 0.000
## IWB07 0.838 0.081 10.331 0.000
## IWB08 0.861 0.161 5.337 0.000
## IWB09 0.833 0.148 5.644 0.000
## Head =~
## SN01 1.000
## SN02 1.199 0.125 9.619 0.000
## SN03 1.019 0.131 7.752 0.000
## SN04 1.175 0.142 8.304 0.000
## SN05 1.039 0.158 6.560 0.000
## SN07 1.139 0.139 8.207 0.000
## SN08 1.039 0.115 9.035 0.000
## SN09 1.004 0.151 6.668 0.000
## SN10 1.106 0.133 8.341 0.000
## SN11 1.022 0.127 8.030 0.000
## SN12 1.047 0.137 7.669 0.000
## SN18 1.210 0.145 8.326 0.000
## Heart =~
## SN13 1.000
## SN14 0.446 0.187 2.388 0.017
## SN15 0.955 0.090 10.649 0.000
## SN16 0.869 0.096 9.047 0.000
## SN17 1.123 0.149 7.534 0.000
## Hand =~
## SN20 1.000
## SN21 0.926 0.086 10.761 0.000
## SN22 0.968 0.079 12.298 0.000
## SN23 0.848 0.101 8.354 0.000
## SN24 0.987 0.089 11.144 0.000
## SN25 0.987 0.111 8.868 0.000
## SN26 0.930 0.113 8.193 0.000
## SN27 1.089 0.104 10.437 0.000
## SN28 0.969 0.099 9.763 0.000
## SN30 0.849 0.095 8.930 0.000
## SN31 0.981 0.108 9.072 0.000
## SN32 1.019 0.082 12.459 0.000
## SN33 1.058 0.085 12.493 0.000
## SN34 0.968 0.091 10.605 0.000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## IWB ~
## Hand (a) 0.981 0.115 8.529 0.000
## Hand ~
## Head (d) 0.828 0.105 7.912 0.000
## Heart (b) 0.271 0.106 2.548 0.011
## Heart ~
## Head (c) 0.890 0.155 5.758 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .IWB07 ~~
## .SN24 0.169 0.069 2.461 0.014
## .IWB03 ~~
## .SN16 -0.129 0.038 -3.404 0.001
## .SN02 ~~
## .SN30 -0.090 0.032 -2.784 0.005
## .SN04 ~~
## .SN31 -0.111 0.053 -2.095 0.036
## .SN05 ~~
## .SN30 0.053 0.038 1.413 0.158
## .SN12 ~~
## .SN21 0.059 0.031 1.873 0.061
## .SN13 ~~
## .SN20 -0.089 0.047 -1.868 0.062
## .SN15 ~~
## .SN24 -0.098 0.038 -2.555 0.011
## .SN16 ~~
## .SN20 -0.086 0.057 -1.499 0.134
## .SN21 ~~
## .SN34 -0.070 0.034 -2.047 0.041
## .SN22 0.081 0.034 2.395 0.017
## .SN24 ~~
## .SN28 -0.106 0.042 -2.508 0.012
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .IWB01 0.271 0.049 5.495 0.000
## .IWB02 0.430 0.063 6.804 0.000
## .IWB03 0.421 0.067 6.280 0.000
## .IWB04 0.484 0.067 7.200 0.000
## .IWB05 0.360 0.057 6.342 0.000
## .IWB06 0.558 0.123 4.522 0.000
## .IWB07 0.554 0.094 5.874 0.000
## .IWB08 0.522 0.085 6.125 0.000
## .IWB09 0.596 0.091 6.524 0.000
## .SN01 0.350 0.111 3.149 0.002
## .SN02 0.273 0.088 3.088 0.002
## .SN03 0.288 0.073 3.950 0.000
## .SN04 0.316 0.082 3.832 0.000
## .SN05 0.305 0.072 4.222 0.000
## .SN07 0.262 0.070 3.736 0.000
## .SN08 0.256 0.045 5.753 0.000
## .SN09 0.239 0.058 4.093 0.000
## .SN10 0.263 0.052 5.064 0.000
## .SN11 0.239 0.043 5.523 0.000
## .SN12 0.239 0.071 3.387 0.001
## .SN18 0.352 0.094 3.757 0.000
## .SN13 0.226 0.066 3.455 0.001
## .SN14 0.406 0.087 4.679 0.000
## .SN15 0.218 0.064 3.424 0.001
## .SN16 0.269 0.064 4.225 0.000
## .SN17 0.122 0.067 1.840 0.066
## .SN20 0.314 0.059 5.348 0.000
## .SN21 0.214 0.037 5.777 0.000
## .SN22 0.214 0.038 5.594 0.000
## .SN23 0.307 0.079 3.875 0.000
## .SN24 0.313 0.077 4.059 0.000
## .SN25 0.351 0.068 5.176 0.000
## .SN26 0.333 0.077 4.319 0.000
## .SN27 0.154 0.041 3.763 0.000
## .SN28 0.289 0.062 4.665 0.000
## .SN30 0.202 0.038 5.244 0.000
## .SN31 0.195 0.043 4.568 0.000
## .SN32 0.463 0.187 2.473 0.013
## .SN33 0.218 0.051 4.269 0.000
## .SN34 0.198 0.040 4.977 0.000
## .IWB 0.044 0.042 1.066 0.286
## Head 0.767 0.276 2.775 0.006
## .Heart 0.191 0.065 2.956 0.003
## .Hand 0.007 0.011 0.601 0.548
##
## R-Square:
## Estimate
## IWB01 0.770
## IWB02 0.644
## IWB03 0.661
## IWB04 0.469
## IWB05 0.660
## IWB06 0.564
## IWB07 0.536
## IWB08 0.564
## IWB09 0.514
## SN01 0.687
## SN02 0.802
## SN03 0.734
## SN04 0.770
## SN05 0.731
## SN07 0.792
## SN08 0.764
## SN09 0.764
## SN10 0.781
## SN11 0.771
## SN12 0.779
## SN18 0.762
## SN13 0.779
## SN14 0.282
## SN15 0.770
## SN16 0.692
## SN17 0.892
## SN20 0.741
## SN21 0.782
## SN22 0.797
## SN23 0.678
## SN24 0.737
## SN25 0.714
## SN26 0.700
## SN27 0.873
## SN28 0.745
## SN30 0.762
## SN31 0.816
## SN32 0.668
## SN33 0.822
## SN34 0.810
## IWB 0.951
## Heart 0.761
## Hand 0.993
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|)
## EffHnd 0.981 0.115 8.529 0.000
## EffHrt 0.266 0.096 2.783 0.005
## EffHed 1.049 0.140 7.509 0.000# modificationIndices(Fit05, minimum.value = 5)5.6 Plot Model (WLSMV) - 76 Raters
# Loading necessary packages
if(! "semPlot" %in% installed.packages()) {install.packages("semPlot", dependencies = TRUE) }
library(semPlot)
# Setting working Directory
setwd("~/AB PRIVATE/01 Amy/AB Amy PhD/Part 3/Data/Study3")
# Prepare PDF for Model 05
if (makePDF) {
pdf(paste(today, "Model05.pdf"), width = 25, height = 25)
}
par(mar=c(7, 1, 7, 1))
par(oma=c(1, 1, 1, 1))
# Prepare fitmeasures
ParDF <- as.data.frame(do.call(cbind, Fit05@ParTable))
EffHed <- round(as.numeric(ParDF[ParDF$label == "EffHed", 14]), 4)
EffHrt <- round(as.numeric(ParDF[ParDF$label == "EffHrt", 14]), 4)
EffHnd <- round(as.numeric(ParDF[ParDF$label == "EffHnd", 14]), 4)
n <- Fit05@SampleStats@ntotal
fitMeas <- toString(c("ChiSq: ", round(as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "chisq"))), 4),
" - ChiSq-p: ", round(as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "pvalue"))), 4),
" - DF: ", gsub("[^0-9.]", "", fitMeasures(Fit05, "df")),
" - ChiSq/DF: ", round(as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "chisq")))/ as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "df"))), 4),
" - CFI: ", round(as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "cfi"))), 4),
" - TLI: ", round(as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "tli"))), 4),
" - RMSEA: ", round(as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "rmsea"))), 4),
" - SRMR: ", round(as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "srmr"))), 4),
" - n: ", n,
" - EffHed: ", EffHed,
" - EffHrt: ", EffHrt,
" - EffHnd: ", EffHnd
),
width = 255)
fitMeas <- gsub(",", "", fitMeas)
# Plot model
semPaths(Fit05, what = "eq", whatLabels = "stand", intercepts = FALSE, residuals = TRUE,
edge.label.cex = 0.7, edge.color = "blue", layout = "circle2", rotation = 3, curve = 1, curvePivot = TRUE, mar = c(3,1,5,1), sizeLat = 7, sizeMan = 4, color = colorlist,
style = "lisrel")
title(main = "Model 5: Showing Head -> Hand -> IWB with Heart as Mediator\nEstimator: WLSMV - 76 Raters",
cex.main = 2.5, col.main = "darkblue", font.main = 3, sub = fitMeas, cex.sub = 1.4)
if (makePDF) {
dev.off()
}5.7 Build Model: Head -> Hand -> IWB with Heart as Mediator (DWLS) - 76 Raters
# Loading necessary packages
if(! "lavaan" %in% installed.packages()) {install.packages("lavaan", dependencies = TRUE) }
library(lavaan)
Model05 <- '
# latent variables
IWB =~ IWB01 + IWB02 + IWB03 + IWB04 + IWB05 + IWB06 + IWB07 + IWB08 + IWB09
Head =~ SN01 + SN02 + SN03 + SN04 + SN05 + SN07 + SN08 + SN09 + SN10 + SN11 + SN12
Heart =~ SN13 + SN14 + SN15 + SN16 + SN17 + SN18
Hand =~ SN20 + SN21 + SN22 + SN23 + SN24 + SN25 + SN26 + SN27 + SN28 + SN30 + SN31 + SN32 + SN33 + SN34
# direct effect
IWB ~ a * Hand
Hand ~ d * Head
EffHnd := a
# mediator
Hand ~ b * Heart
Heart ~ c * Head
# indirect effect
EffHrt := a * b
EffHed := a * (d + b * c)
'
# Calculate fit
Fit05 <- sem(Model05, data = dfVal, estimator = "DWLS")
# Print results (fit indices, parameters, hypothesis tests)
summary(Fit05, fit.measures = TRUE, rsquare = TRUE)## lavaan 0.6-12 ended normally after 74 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of model parameters 84
##
## Number of observations 76
##
## Model Test User Model:
##
## Test statistic 42.202
## Degrees of freedom 736
## P-value (Chi-square) 1.000
##
## Model Test Baseline Model:
##
## Test statistic 9475.041
## Degrees of freedom 780
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.085
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value RMSEA <= 0.05 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.042
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## IWB =~
## IWB01 1.000
## IWB02 0.924 0.061 15.275 0.000
## IWB03 0.946 0.055 17.171 0.000
## IWB04 0.685 0.044 15.677 0.000
## IWB05 0.877 0.055 15.898 0.000
## IWB06 0.892 0.053 16.790 0.000
## IWB07 0.843 0.055 15.364 0.000
## IWB08 0.861 0.053 16.166 0.000
## IWB09 0.833 0.053 15.856 0.000
## Head =~
## SN01 1.000
## SN02 1.197 0.080 15.007 0.000
## SN03 1.019 0.068 14.924 0.000
## SN04 1.171 0.080 14.559 0.000
## SN05 1.041 0.074 14.016 0.000
## SN07 1.140 0.076 14.909 0.000
## SN08 1.040 0.071 14.564 0.000
## SN09 1.005 0.072 14.018 0.000
## SN10 1.106 0.075 14.825 0.000
## SN11 1.022 0.070 14.508 0.000
## SN12 1.050 0.073 14.353 0.000
## Heart =~
## SN13 1.000
## SN14 0.448 0.037 12.008 0.000
## SN15 0.955 0.070 13.577 0.000
## SN16 0.861 0.068 12.756 0.000
## SN17 1.127 0.080 14.037 0.000
## SN18 1.276 0.089 14.409 0.000
## Hand =~
## SN20 1.000
## SN21 0.932 0.061 15.242 0.000
## SN22 0.974 0.063 15.478 0.000
## SN23 0.851 0.058 14.729 0.000
## SN24 0.992 0.065 15.302 0.000
## SN25 0.991 0.068 14.651 0.000
## SN26 0.934 0.064 14.694 0.000
## SN27 1.094 0.070 15.703 0.000
## SN28 0.970 0.063 15.377 0.000
## SN30 0.851 0.059 14.541 0.000
## SN31 0.981 0.064 15.308 0.000
## SN32 1.024 0.066 15.486 0.000
## SN33 1.063 0.068 15.586 0.000
## SN34 0.970 0.064 15.183 0.000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## IWB ~
## Hand (a) 0.986 0.065 15.224 0.000
## Hand ~
## Head (d) 0.736 0.308 2.389 0.017
## Heart (b) 0.362 0.321 1.127 0.260
## Heart ~
## Head (c) 0.895 0.080 11.245 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .IWB01 0.271 0.256 1.058 0.290
## .IWB02 0.430 0.247 1.739 0.082
## .IWB03 0.427 0.174 2.450 0.014
## .IWB04 0.484 0.136 3.555 0.000
## .IWB05 0.360 0.194 1.854 0.064
## .IWB06 0.558 0.214 2.609 0.009
## .IWB07 0.546 0.185 2.943 0.003
## .IWB08 0.522 0.251 2.079 0.038
## .IWB09 0.596 0.244 2.446 0.014
## .SN01 0.347 0.293 1.186 0.236
## .SN02 0.273 0.292 0.935 0.350
## .SN03 0.285 0.234 1.219 0.223
## .SN04 0.319 0.355 0.900 0.368
## .SN05 0.299 0.315 0.948 0.343
## .SN07 0.257 0.277 0.928 0.354
## .SN08 0.252 0.255 0.987 0.324
## .SN09 0.235 0.290 0.810 0.418
## .SN10 0.259 0.264 0.979 0.327
## .SN11 0.236 0.248 0.950 0.342
## .SN12 0.232 0.269 0.860 0.390
## .SN13 0.285 0.290 0.984 0.325
## .SN14 0.416 0.115 3.615 0.000
## .SN15 0.272 0.243 1.118 0.263
## .SN16 0.323 0.252 1.280 0.201
## .SN17 0.189 0.291 0.650 0.516
## .SN18 0.270 0.338 0.800 0.423
## .SN20 0.321 0.278 1.152 0.249
## .SN21 0.210 0.259 0.813 0.416
## .SN22 0.209 0.270 0.775 0.438
## .SN23 0.306 0.260 1.178 0.239
## .SN24 0.311 0.271 1.147 0.252
## .SN25 0.350 0.369 0.948 0.343
## .SN26 0.332 0.293 1.130 0.258
## .SN27 0.153 0.309 0.496 0.620
## .SN28 0.293 0.254 1.155 0.248
## .SN30 0.203 0.264 0.770 0.441
## .SN31 0.200 0.285 0.702 0.482
## .SN32 0.462 0.333 1.385 0.166
## .SN33 0.217 0.297 0.731 0.465
## .SN34 0.200 0.267 0.750 0.453
## .IWB 0.042 0.051 0.831 0.406
## Head 0.770 0.080 9.618 0.000
## .Heart 0.124 0.083 1.493 0.135
## .Hand 0.010 0.039 0.250 0.802
##
## R-Square:
## Estimate
## IWB01 0.770
## IWB02 0.643
## IWB03 0.656
## IWB04 0.469
## IWB05 0.660
## IWB06 0.564
## IWB07 0.542
## IWB08 0.564
## IWB09 0.514
## SN01 0.689
## SN02 0.801
## SN03 0.738
## SN04 0.768
## SN05 0.737
## SN07 0.795
## SN08 0.767
## SN09 0.768
## SN10 0.785
## SN11 0.774
## SN12 0.785
## SN13 0.722
## SN14 0.263
## SN15 0.713
## SN16 0.630
## SN17 0.832
## SN18 0.817
## SN20 0.735
## SN21 0.786
## SN22 0.802
## SN23 0.678
## SN24 0.738
## SN25 0.714
## SN26 0.701
## SN27 0.874
## SN28 0.741
## SN30 0.760
## SN31 0.811
## SN32 0.669
## SN33 0.823
## SN34 0.807
## IWB 0.954
## Heart 0.832
## Hand 0.989
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|)
## EffHnd 0.986 0.065 15.224 0.000
## EffHrt 0.357 0.317 1.128 0.259
## EffHed 1.046 0.082 12.733 0.000modificationIndices(Fit05, minimum.value = 5)## [1] lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## <0 rows> (or 0-length row.names)5.8 Plot Model - (DWLS) 76 Raters
# Loading necessary packages
if(! "semPlot" %in% installed.packages()) {install.packages("semPlot", dependencies = TRUE) }
library(semPlot)
# Setting working Directory
setwd("~/AB PRIVATE/01 Amy/AB Amy PhD/Part 3/Data/Study3")
# Prepare PDF for Model 05
if (makePDF) {
pdf(paste(today, "Model05.pdf"), width = 25, height = 25)
}
par(mar=c(7, 1, 7, 1))
par(oma=c(1, 1, 1, 1))
# Prepare fitmeasures
ParDF <- as.data.frame(do.call(cbind, Fit05@ParTable))
EffHed <- round(as.numeric(ParDF[ParDF$label == "EffHed", 14]), 4)
EffHrt <- round(as.numeric(ParDF[ParDF$label == "EffHrt", 14]), 4)
EffHnd <- round(as.numeric(ParDF[ParDF$label == "EffHnd", 14]), 4)
n <- Fit05@SampleStats@ntotal
fitMeas <- toString(c("ChiSq: ", round(as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "chisq"))), 4),
" - ChiSq-p: ", round(as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "pvalue"))), 4),
" - DF: ", gsub("[^0-9.]", "", fitMeasures(Fit05, "df")),
" - ChiSq/DF: ", round(as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "chisq")))/ as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "df"))), 4),
" - CFI: ", round(as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "cfi"))), 4),
" - TLI: ", round(as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "tli"))), 4),
" - RMSEA: ", round(as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "rmsea"))), 4),
" - SRMR: ", round(as.numeric(gsub("[^0-9.]", "", fitMeasures(Fit05, "srmr"))), 4),
" - n: ", n,
" - EffHed: ", EffHed,
" - EffHrt: ", EffHrt,
" - EffHnd: ", EffHnd
),
width = 255)
fitMeas <- gsub(",", "", fitMeas)
# Plot model
semPaths(Fit05, what = "eq", whatLabels = "stand", intercepts = FALSE, residuals = TRUE,
edge.label.cex = 0.7, edge.color = "blue", layout = "circle2", rotation = 3, curve = 1, curvePivot = TRUE, mar = c(3,1,5,1), sizeLat = 7, sizeMan = 4, color = colorlist,
style = "lisrel")
title(main = "Model 5: Showing Head -> Hand -> IWB with Heart as Mediator\nEstimator: DWLS - 76 Raters",
cex.main = 2.5, col.main = "darkblue", font.main = 3, sub = fitMeas, cex.sub = 1.4)
if (makePDF) {
dev.off()
}