Plausible Values as Predictors

Although the mixPV function was introduced as a way to analyze large scale assessments using multiple plausible values (PV), the function only works if the plausible values are used as the outcome (i.e., it is the Y variable or on the left hand side [LHS] of the equation). However, there are times when the PV is the predictor of interest. This still has to be analyzed properly (i.e., just don’t average all the values).

Shown below are the steps (using a kind of nonsensical example) how to do this manually. The mixPV function is still needed in order to properly pool the results though.

We’ll ask the research question if SES (escs) and math performance (math; five PVs) can predict math interest (e.g., look forward to lessons). I know, the directionality of this is unclear but this is for illustrative purposes only.

library(MLMusingR)
data(pisa2012)

Using the dataset, we’ll need to convert it into a tall dataset and then convert it into a list object. We’ll use the tidyr package:

library(tidyr)
tall <- pivot_longer(pisa2012, pv1math:pv5math, names_to = 'pv',
                     values_to = 'math')

We’ll turn the categorical outcome into a continuous one for this example:

tall$mathinterest <- 4 - as.numeric(tall$st29q03) #outcome of interest
# Maths interest- Look forward to lessons
table(tall$mathinterest, tall$st29q03) #just checking

   
    Strongly agree Agree Disagree Strongly disagree  N/A Invalid Missing
  0              0     0        0              2405    0       0       0
  1              0     0     6155                 0    0       0       0
  2              0  5185        0                 0    0       0       0
  3           1935     0        0                 0    0       0       0

## make into a list to be analyzed separately
dat <- split(tall, tall$pv)

Once we have our data stored as a list object, we can use the mix function in the WeMix package to analyze each dataset (there are five, one for each PV). I just standardize (z score) the math ability as well:

library(WeMix)
WeMix v4.0.3

m1 <- \(x) { #change this function to what you are interested in
  mix(mathinterest ~ scale(math) + escs + (1|schoolid), 
        weights = c('w_fstuwt', 'w_fschwt'),
        data = x)
}
res <- lapply(dat, m1)

The results are stored in the res object as a list. This still needs to be pooled properly. To do that, we have to make the output something that mixPV can understand and pool the results:

class(res) <- 'mixPV' #need this to pool results
summary(res)

Results of multilevel analyses with 5 plausible values.
Number of observations: 3136 

Estimates for random effects: 
                     estimate std.error statistic   df Pr(>t)    
schoolid.(Intercept)   0.0942    0.0198    4.7544 3097 <2e-16 ***
Residual               0.7143    0.0200   35.7462 2837 <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Estimates for fixed effects: 
            estimate std.error statistic   df Pr(>t)    
(Intercept)   1.3995    0.0478   29.2881 3118 <2e-16 ***
scale(math)   0.1468    0.0235    6.2461  136 <2e-16 ***
escs         -0.0149    0.0229   -0.6499 2315   0.52    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

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