How to replicate Principal Component Analysis Components/Dimensions using R and Excel – Displayr Help

This article describes replicating the calculation of Components/Dimensions values derived from the Principal Component Analysis analysis in Displayr. The final output matches the values created by Displayr when following the steps outlined here: How to Save Components/Dimensions from a Dimension Reduction Output.

Requirements

A dimension reduction output created in Displayr such as Principal Component Analysis, Correspondence Analysis, Multidimensional Scaling or t-SNE.
See: How to Do Principal Component Analysis in Displayr.

Method

OPTIONAL: The below steps assume that the Principal Component Analysis is weighted. If you don't require a weight, you can create a weight of 1 for all respondents. This will return the same outputs as an unweighted analysis.
1. Hover over the Data Sets tree and select + > Custom Code > JavaScript - Numeric.
2. Input a value of 1 into the JAVASCRIPT CODE window.
3. Select Usable as a weight.
4. Select the PCA output, go to Inputs > FILTERS & WEIGHTS, and select the Weight from the drop-down.

The first step of the process requires us to obtain the respondent data and weights from the PCA analysis and compute the weighted mean and standard deviation.

Select Calculation > Custom Code from the toolbar and draw an output on the page.

Go to Properties > R Code and input the below code:

#Define your input mode name
input.model = dim.reduce

#Obtain the respondent level data and weights
respondent.data = input.model$data.used$subset.data
weights = input.model$data.used$subset.weights

#Function to calculate the weighted response level data and standard devition 
weightedMeanAndSD <- function(x, weights)
{
    complete.cases <- !is.na(x) & weights > 0
    wx <- x * weights
    weighted.mean <- Sum(wx[complete.cases], remove.missing = FALSE) / Sum(weights[complete.cases], remove.missing = FALSE)
    sx <- x - weighted.mean
    wsx2 <- weights * sx * sx
    weighted.variance <- Sum(wsx2[complete.cases], remove.missing = FALSE) / (Sum(weights[complete.cases], remove.missing = FALSE) - 1)
    return(list(weighted.mean = weighted.mean, weighted.sd = sqrt(weighted.variance)))
}

weighted.mean.and.sd = lapply(respondent.data, FUN = function(x, weights) { unlist(weightedMeanAndSD(x, weights)) }, weights = weights)

#Return the table wihh the outputs
weighted.mean.and.sd = do.call(rbind, weighted.mean.and.sd)

Note: the first of the code assumes the PCA output is called dim.reduce.

The code will return an output like the one below. Select the output and select Copy > Copy Data from the toolbar.
Paste the data into Excel.

Next, we will need to obtain the score weights from the PCA.
1. Select Calculation > Custom Code from the toolbar and draw an output on the page.
2. Go to Properties > R Code and input the below code:
```
#Define your input mode name
input.model = dim.reduce

#Obtain the weights
score.weights = input.model$score.weights
```
3. The code will return an output like the one below. Select the output and select Copy > Copy Data from the toolbar.
4. Paste the data into Excel.
In the next step, we will obtain the respondent-level data used in the PCA.
1. Select Calculation > Custom Code from the toolbar and draw an output on the page.
2. Go to Properties > R Code and input the below code: dim.reduce$data.used.
3. Select the output and select Copy > Copy Data from the toolbar.
4. Paste the data into Excel.
For each component, do the sum-product of the scaled respondent data and the component scores for that component (see Excel file with Calculations).
To check the values match those obtained using Save Variable(s) > Components/ Dimensions. , select Scores from dim.reduce variable set from the Data Sets tree, right-click > Show in Data Editor.