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 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. To create a weight of 1 for all respondents:

1. Hover over the Data Sources tree and select + > Custom Code > JavaScript - Numeric.
2. Input a value of 1 into the JavaScript Code window.
3. Click Calculate.
4. Select Usable as a weight.
5. Select the PCA output, 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.

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

Input the below code 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 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 Tools menu in the upper left corner.
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. Input the below code in the R code editor:
```
#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. In the R code editor, paste: 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 Sources tree, right-click > View in Data Editor.