How to Replicate Components/Dimensions from Principal Component Analysis 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

The steps below 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. To create a weight of 1 for all respondents:

Hover over the Data Sources tree and select + > Custom Code > JavaScript - Numeric.
Input a value of 1 into the JavaScript Code editor.
Click Calculate in the object inspector .
Tick Usable as a weight in the object inspector .
Select the PCA output, and from the object inspector , go to Data > Filters & Weight, 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.

From the toolbar, select Calculation > Custom Code and click on the page to place the output.

Input the code below in the R code editor:

#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 part of the code assumes the PCA output is called dim.reduce.

The code will return an output like the one below. Select the output, right-click, and select Copy > Copy Data.
Paste the data into Excel.

Next, we will need to obtain the score weights from the PCA.

From the toolbar, select Calculation > Custom Code and click on the page to place the output.

Input the code below in the R code editor:

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

#Obtain the weights
score.weights = input.model$score.weights

The code will return an output like the one below. Select the output, right-click, and select Copy > Copy Data.
Paste the data into Excel.

In the next step, we will obtain the respondent-level data used in the PCA.

From the toolbar, select Calculation > Custom Code and click on the page to place the output.
In the R code editor, paste: dim.reduce$data.used.
Select the output, right-click, and select Copy > Copy Data.
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 in the object inspector: