Score-based Tests

Andreas M. Brandmaier

2021-06-11

Load data

Load affect dataset from the psychTools package. These are data from two studies conducted in the Personality, Motivation and Cognition Laboratory at Northwestern University to study affect dimensionality and the relationship to various personality dimensions. In the following code, we replace the numeric film labels with the movie titles. Also, we select a subset of predictors including the film, personality dimensions, trait anxiety and affect before having watched the movie.

library(psychTools)
data(affect)

affect$Film <- factor(affect$Film, ordered = FALSE, 
                      labels=c("Frontline", "Halloween", "Nat. Geographic","Parenthood"))


tree.data <- affect[,c("Film","neur","ext","soc","traitanx","NA1","PA1")] 
tree.data$DeltaPA <- affect$PA2-affect$PA1

knitr::kable(head(tree.data))
Film neur ext soc traitanx NA1 PA1 DeltaPA
Nat. Geographic 9 18 10 24 2 26 -19
Nat. Geographic 12 16 8 41 4 10 -5
Nat. Geographic 5 6 1 37 2 4 -1
Nat. Geographic 15 12 6 54 0 1 -1
Nat. Geographic 2 14 6 39 13 7 9
Frontline 15 6 4 51 1 5 -3

Create simple model of state anxiety

Here, we create a simple SEM with a single observed variable. No latent variables - only two parameters: mean of DeltaPA and variance of DeltaPA.

library(OpenMx)
manifests<-c("DeltaPA")
latents<-c()
model <- mxModel("Simple Model", 
type="RAM",
manifestVars = manifests,
latentVars = latents,
mxPath(from="one",to=manifests, free=c(TRUE), value=c(1.0) , arrows=1, label=c("mu") ),
mxPath(from=manifests,to=manifests, free=c(TRUE), value=c(1.0) , arrows=2, label=c("sigma2") ),
mxData(tree.data, type = "raw")
);

result <- mxRun(model)
#> Running Simple Model with 2 parameters
summary(result)
#> Summary of Simple Model 
#>  
#> free parameters:
#>     name matrix     row     col    Estimate Std.Error A
#> 1 sigma2      S DeltaPA DeltaPA 27.90300741 2.1722417  
#> 2     mu      M       1 DeltaPA  0.09514715 0.2907414 !
#> 
#> Model Statistics: 
#>                |  Parameters  |  Degrees of Freedom  |  Fit (-2lnL units)
#>        Model:              2                    328              2034.982
#>    Saturated:              2                    328                    NA
#> Independence:              2                    328                    NA
#> Number of observations/statistics: 330/330
#> 
#> Information Criteria: 
#>       |  df Penalty  |  Parameters Penalty  |  Sample-Size Adjusted
#> AIC:      1378.9818               2038.982                 2039.018
#> BIC:       132.8794               2046.580                 2040.236
#> CFI: NA 
#> TLI: 1   (also known as NNFI) 
#> RMSEA:  0  [95% CI (NA, NA)]
#> Prob(RMSEA <= 0.05): NA
#> To get additional fit indices, see help(mxRefModels)
#> timestamp: 2021-06-11 14:04:22 
#> Wall clock time: 0.01559615 secs 
#> optimizer:  SLSQP 
#> OpenMx version number: 2.19.5 
#> Need help?  See help(mxSummary)

Score-based Tests

Use score-based tests to create the tree. Use Bonferroni-correction to adjust for multiple testing of predictors.

library(semtree)
ctrl = semtree.control(
  method="score", 
  bonferroni = TRUE)
tree = semtree( model = result, 
                data = tree.data, 
                control=ctrl)
#> ✔ Tree construction finished [took 2s].

Now let us plot the tree.

plot(tree)

Implied mixture model:

tndata <- semtree::getTerminalNodes(tree)

cols <- viridis::plasma(nrow(tndata))

pl <- ggplot2::ggplot(data = data.frame(x = c(-20, 20)), ggplot2::aes(x))+
  ggplot2::xlab("Change in Positive Affect")
for (i in 1:nrow(tndata)) {
  pl <- pl + ggplot2::stat_function(fun = dnorm, 
      n = 101, col=cols[i], args = list(mean = tndata[i,2], 
                                        sd = sqrt(tndata[i,1])))
}

plot(pl)

Let’s inspect the group with the largest negative change:

i <- which.min(tndata$mu)

pl <- pl +ggplot2::geom_area(stat = "function", 
                             fun = function(x){dnorm(x,mean=tndata[i,2],sd=sqrt(tndata[i,1]))}, 
                             fill = cols[i])+
      ggplot2::geom_label(x=-10,y=.12, label="People with very high positive \naffect, which then watched\n a war film")

plot(pl)