Session 4 - Perceptual Maps: R code and HW

Update:

Folks, the Session 4 HW is due on 14-Dec Friday (and not 10-December as was mistakenly stated in my email). Sorry about the confusion.

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Hi all,

I hope you had the chance to run the R demo of session 3 at home just to see first-hand R's ease-of-use in MKTR.

Before jumping into the R code for Session 3, first, a small admin step - you need to know how to download and install packages in R.

Say, you need the package 'MASS' installed. For the menu-driven option, go to the Packages Menu in the Menu bar, click on 'Install Package(s)...', a window will open asking which server to download the package from. Be patriotic and choose 'India' for our sole R repositary based in IIT-Chennai. Or choose any other country if the desi server is slow at a particular time.

A second window will open listing all the packages in R (at present, this list grows every month) in alphabetical order. Click on the package you want and sit back. R will automatically download and install the package for you. Might take a minute or two at most.

Well, either that or simply type:

install.packages("MASS")

OK, let's get started with the R codes then.

1. Simple Data Visualization using biplots. We use USArrests data (inbuilt R dataset) to see how it can be visualized in 2 dimensions. Just copy-paste the code below onto the R console [Hit 'enter' after the last line].

pc.cr <-princomp(USArrests, cor = TRUE)# scale data summary(pc.cr) biplot(pc.cr)

This is what the plot should look like. Click on image for larger view.

2. Code for making Joint Space maps I have coded a user-defined function called JSM in R. You can use it whenever you need to make joint space maps provided just by invoking the function. All it requires to work is a perceptions table and a preference rating table.

First copy-paste the entire block of code below onto your R console. Those interested in reading the code, pls copy-paste line-by-line. I have put explanations in comments ('#') for what the code is doing.

## --- Build func to run simple perceptual maps --- ## JSM <- function(inp1, prefs){ # inp1 = perception matrix with row and column headers # brands in rows and attributes in columns # prefs = preferences matrix par(pty="s") # set square plotting region fit = prcomp(inp1, scale.=TRUE) # extract prin compts plot(fit$rotation[,1:2], # use only top 2 prinComps type ="n",xlim=c(-1.5,1.5), ylim=c(-1.5,1.5), # plot parms main ="Joint Space map - Home-brew on R") # plot title abline(h=0); abline(v=0) # build horiz & vert axes attribnames = colnames(inp1) brdnames = rownames(inp1) # <-- insert attrib vectors as arrows-- for (i1 in 1:nrow(fit$rotation)){ arrows(0,0, x1=fit$rotation[i1,1]*fit$sdev[1], y1=fit$rotation[i1,2]*fit$sdev[2], col="blue", lwd=1.5); text(x=fit$rotation[i1,1]*fit$sdev[1],y=fit$rotation[i1,2]*fit$sdev[2], labels=attribnames[i1],col="blue", cex=1.1)} # <--- make co-ords within (-1,1) frame # fit1=fit fit1$x[,1]=fit$x[,1]/apply(abs(fit$x),2,sum)[1] fit1$x[,2]=fit$x[,2]/apply(abs(fit$x),2,sum)[2] points(x=fit1$x[,1], y=fit1$x[,2], pch=19, col="red") text(x=fit1$x[,1], y=fit1$x[,2], labels=brdnames,col="black", cex=1.1) # --- add preferences to map ---# k1 = 2; #scale-down factor pref=data.matrix(prefs)# make data compatible pref1 = pref %*% fit1$x[,1:2] for (i1 in 1:nrow(pref1)){segments(0,0, x1=pref1[i1,1]/k1,y1=pref1[i1,2]/k1, col="maroon2", lwd=1.25)} # voila, we're done! # }

3. OfficeStar MEXL example done on R

All the data for the below JSM examples are stored as tables in this google spreadsheet.

I use as my example the OfficeStar dataset that I also demo in class from MEXL's built-in examples database.To facilitate comparison, I use as input format in R the same tables that you would otherwise use in MEXL

Pls open the google doc and copy the average perceptions matrix (cell B5 to cell F10) onto a notepad and read it in the usual way.

Step 3a: Read in the attribute table into 'mydata'.

# -- Read in Average Perceptions table -- # mydata = read.table(file.choose(), header = TRUE) mydata = t(mydata) #transposing to ease analysis mydata #view the table read # extract brand & attribute names # brdnames = rownames(mydata) attribnames = colnames(mydata)

Step 3b: Read into R the preferences table into 'prefs' (cell C15 to F24 on the google spreadsheet) via the notepad.

# -- Read in preferences table -- # pref = read.table(file.choose()) dim(pref) #check table dimensions pref[1:10,] #view first 10 rows

Data reading is done. You should see the data read-in as in the figure above. We can start analysis now. Finally.

Step 3c: Run Analysis

JSM(mydata, pref)

That is it. That one function call executes the entire JSM sequence. The result can be seen in the image below. Again, the JSM function is generic and can be applied to *any* dataset in the input format we just saw to make joint space maps from.

4. Session 2 HW - JSM Analysis

This is *your* data from the session 2 HW surveys you had filled. You evaluated term 4 core courses along 5 attributes. Let's see if a JSM can throw more light on the perceptions and preferences of the Co2013 at Mohali in this regard.

First, read-in the data the usual way.

• Read-in cells M5 to AF55 for the attribute perceptions matrix.
• Then read-in cells H5 to K55 for the preferences matrix.
• Note that the data format here is different from the input in the OfficeStar example. There we had the 'Average perceptions matrix'.
• Here, the data is more 'raw'. It has to be processed and the averages computed and then tabulated. No problemo, we'll get R to process it for us.
• Hence, I have separately entered the attribute and 'brand' names.

# now read in perceptions data (w/o headers) mydata = read.table(file.choose()) dim(mydata); mydata[1:4,] # read-in preferences matrix prefs = read.table(file.choose()) dim(prefs); prefs[1:4,] # name brands and attributes involved attribs = c("PerspChange", "TheoryValue", "PracticalRelevance", "InterestStimulated", "DifficultyLevel") brands = c("GSB", "INVA", "MGTO", "SAIT")

Note above that the attribute and brand names have no spaces in them.

Now, some more code to manipulate the data and build the input matrix in the right format. On your part, just copy-paste. if you want to understand the code, go line-by-line, else paste in a block.

# Build input matrix for Perceptual map inp1 = matrix(0, nrow=length(attribs), ncol=length(brands)) a1 = apply(mydata, 2, mean) a2 = seq(from=1, to=20, by=4) for (i1 in 1:nrow(inp1)){ inp1[i1,] = a1[a2[i1]:(a2[i1]+ncol(inp1)-1)]} colnames(inp1) = brands; rownames(inp1) = attribs; inp1 inp1 = t(inp1) # transpose for convenience cor(inp1) # view correlations among the attribs

OK. Now to run the analysis. Again, just invoke JSM and it does the job.
Note:Use 'inp1' and 'prefs' as arguments to the JSM function because that is what we have named our average perceptions matrix and our preference matrix respectively.

JSM(inp1, prefs)

4. Applying JSM to select Subsets

In Session 4, we see that p-maps can mislead and confuse as much as enlighten. It's important that the transformation (e.g. taking averages) of perceptual data be meaningful. Hence, there may be occasion for us to require that we build JSMs on select subsets of the full dataset.

For instance, if we had reason to believe that males and females may perceive a given brand differently, then could we sort the dataset by gender and draw JSMs by gender?

The below function 'JSMsubset' allows us to sort on any column of interest and plot JSMs for each chosen subset.

### --- func to build inputs to JSM subsets ---- ### JSMsubset <- function(mydata, prefs, attribs, brands, k1){ a1 = apply(mydata[k1,], 2, mean) a2 = seq(from=1, to=length(a1), by=length(brands)) # define a new inp1 inp1 = matrix(0, nrow=length(attribs), ncol=length(brands)) for (i1 in 1:nrow(inp1)){ inp1[i1,] = a1[a2[i1]:(a2[i1]+ncol(inp1)-1)]} colnames(inp1) = brands; rownames(inp1) = attribs; inp1 inp1 = t(inp1) # transpose for convenience prefs1 = prefs[k1,] outp = list(inp1, prefs1) outp }

Henceforth, invoking JSMsubset() will produce an output that will then enable us to use JSM() proper to draw JSMs. Read in the gender variable (cells L5 to L55) into a dataset called 'demog' and follow the code below.

demog=read.table(file.choose()) attach(demog); fem=(Gender=="Female") male=(Gender!="Female") k1 = fem outp = JSMsubset(mydata, prefs, attribs, brands, k1) JSM(outp[[1]], outp[[2]])

That was the female students' p-map. The one for male students follows.

k1 = male outp = JSMsubset(mydata, prefs, attribs, brands, k1) JSM(outp[[1]], outp[[2]])

OK, so I was quite mystified when I noted that the perceptions from Mohali seemed remarkably similar across attributes and courses. In contrast, the Hyd folks were all over the place. Later, it dawned that not all Hyd students had a uniform core courses experience. Different sections had different instructors and so on. Here, one instructor effectively handled all 3 sections.

BTW, how might you use JSMsubset for your coming HW? Well, imagine if you could sort by, say, workex or intended major or any other variable of interest and then draw JSMs. For instance:

k1=(pgid==61310076) outp = JSMsubset(mydata, prefs, attribs, brands, k1) JSM(outp[[1]], outp[[2]]) k1 = (workex > 4) outp = JSMsubset(mydata, prefs, attribs, brands, k1) JSM(outp[[1]], outp[[2]])

The real power of the above method will come after we go through session 5 - segmentation. Once we start segmenting a respondent base using basis variables of interest, then we can use JSMsubset to test around hither-tither.

4a. HW1 for Session 4 involving JSMsubsets.

About the data:

• Open the HW dataset sent by email to you. Go to the worksheet 'HW1 JSM input data'.
• Columns A to Z contain your perception and preference matrices. These data are already there in the google spreadsheet.
• Columns AB to AI contain demographic information - workex(yrs), Gender, Education and Intended major. This is how typical qualtrics output would look like (after cleaning up).

Your task in Session 4 HW1 is to:

• Plot any one student's JSM. Then plot another student's JSM. By trial and error find two students such that their JSMs show significant differences. Interpret the differences.
• Split the Dataset into two - Those intending to major in marketing and Those not. Then plot JSMs for each of these 2 groups. Interpret differences if any.
• Split the Dataset into two - Engineers versus non-engineers. Then plot JSMs for each of these 2 groups. Interpret differences if any.

Submission Format:

• Create a plain white blank PPT
• Write your name and PGID on the title slide
• Copy-paste your JSM plots from R to the PPT(as metafiles)
• After each JSM plot, explain yourinterpretation of the plot in bullet points in the next slide
• Give an informative heading to each slide. E.g., 'JSM for student 10' or 'Interpreting student 10's JSM' etc.
• Use the same format for HW2 and HW3 on MDS and factor analysis
• Drop the PPT into the dropbox on LMS well before deadline (next Friday 14-Dec midnight).

In case you are wondering what is the value-add from this exercise, let me point out the learning goals that should all be well within grasp once you successfully navigate this part of your HW.

Click on the image for a larger size picture.

The MDS and factor analysis components of session 4 are in a separate blog-post as this one was getting unwieldy.

Sudhir