## Introduction

This article shows you how to take discriminant functions produced in one data set and program them to predict segments in a different data set that contains the same variables, or re-use an LDA typing tool that has been given to you as an Excel spreadsheet.

## Requirements

A categorical variable containing the segments you want to predict. If you do not already have one, you can create an analysis like Cluster Analysis or a Latent Class Analysis.

In the example, I’ve run a Latent Class segmentation from a sample of 725 cell phone users. I’ve used the top 2 box scores from a 25 question attitudinal battery as input to the Latent Class Analysis and settled on a 4-class segmentation solution.

## Method

Next, I’ve run a Linear Discriminant Analysis to identify the “golden questions”. LDA is perhaps one of the simpler techniques to use for this purpose as it applies a formula that is easy to understand and program.

- Select
**Create > Classifier > Linear Discriminant Analysis** - In the
**Outcome**box, select the variable that identifies your segments - In the
**Predictor(s)**box, select your predictor variables - Click
**Calculate**.

In this model, I’ve identified 8 of the 25 attitudinal questions, which gives me an 82% segment prediction accuracy. - If you’ve run the Linear Discriminant Analysis in Displayr as I’ve done above, you can then generate the Discriminant Functions by doing the following:
- Select the
**LDA output** - From the menus select
**Create > Classifier > Diagnostic > Table of Discriminant Functions Coefficients****.**This generates the following output:

These can be easily exported to Excel if needed by simply clicking on the Excel icon in the toolbar.

- Select the

### A Word about the Classificiation Algorithm

With the discriminant functions in hand, we can now create the LDA typing tool, but first a word about how to formulate the classification algorithm for each segment.

Each segment takes the form of:

*segmentn = b + (var1 * coeff1) + (var2 * coeff2) + (var3 * coeff3) + . . . . + (varn * coeffn)*

where *b* is the intercept, *varn* represents the variable response and *coeffn* represents the coefficients from the discriminant function.

For example, a respondent who gave a top 2 box score for the first 4 questions but not for the second four questions would result in the following *segment1* value:

*segment1 = -3.5 + (1 * 1.8) + (1 * 3.6) + (1 * 1.2) + (1 * 2.4) + (0 * 0.8) + (0 * 0.4) + (0 * 1.6) + (0 * 1.2) = 5.48*

If we do this for each of the 4 segments, we end up with a value for each segment. We then determine which value is the largest and assign the respondent to the corresponding segment**. **In this example, we find that segment 4 has the highest value, so this respondent is allocated to segment 4.

*segment1 = 5.48**segment2 = 2.31**segment3 = -4.03***segment4 = 5.73**

### Applying the algorithm to another survey

To be able to apply the classification algorithm in another survey, the exact same questions must be present in the new survey. We can then use a little bit of JavaScript to formulate the classification algorithm.

To create the JavaScript variable,

- Go to the
**Variables and Questions**tab - Right-click where you want to add the segment variable
- Select
**Insert Variable(s) > JavaScript Formula > Numeric**. For my example, I add the following JavaScript code into the expression section of the JavaScript window:var segment1 = -3.5 + (q23b * 1.8) + (q23c * 3.6) + (q23h * 1.2) + (q23l * 2.4) + (q23o * 0.8) + (q23u * 0.4) + (q23v * 1.6) + (q23w * 1.2);

The first 4 lines of the JavaScript code above calculates the segment variable for each of the segments using the discriminant functions and the responses to each of the questions. The next line identifies the largest segment value and stores it in a variable called

var segment2 = -6.3 + (q23b * 0.9) + (q23c * 1.3) + (q23h * 1.9) + (q23l * 4.5) + (q23o * 5.7) + (q23u * 1) + (q23v * 0.1) + (q23w * 0.1);

var segment3 = -18.7 + (q23b * 4.1) + (q23c * 3.3) + (q23h * 2.6) + (q23l * 4.6) + (q23o * 1.5) + (q23u * 5.4) + (q23v * 9.1) + (q23w * 12.8);

var segment4 = -12.1 + (q23b * 4.1) + (q23c * 4.2) + (q23h * 4.1) + (q23l * 5.5) + (q23o * 5.6) + (q23u * 1.5) + (q23v * 2.2) + (q23w * 2.2);

maxSegment = Math.max(segment1, segment2, segment3, segment4);

if (maxSegment == segment1) 1;

else if (maxSegment == segment2) 2;

else if (maxSegment == segment3) 3;

else if (maxSegment == segment4) 4;

else NaN;*maxSegment*. The last 4 lines of code check to see which segment value the*maxSegment*matches and returns the corresponding segment. - Click
**Calculate**. This will create a variable that identifies the maxSegment for each case. The segmentation variable based on the classification algorithm is added to your data set.

We can review the **Preview of results** section at the bottom to ensure that the segment values are being returned as expected. Enter a **Name** and **Label** for your new variable, and click **OK** to save the JavaScript variable. The segmentation variable based on the classification algorithm is added to your data set. It’s a good idea to click into the **Question Type** column for this variable and change it to **Pick One** so that any tables will show the segments as categories.

## NEXT

Machine Learning - Linear Discriminant Analysis

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