# POL242Y1 Lecture Notes - Lecture 6: Principal Component Analysis, Latent Variable, Recode

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Week 6-Lecture

Pearson’s R and Spearman’s p

Spearman’s P

As the dots spread out, correlation decreases

The idea of spearman’s row is the same idea as correlation. One of the things we are looking for

is: Logan regression (nonlinear relation)

Assignment #2 Write up

Tablesassessment (explain whether there are relations.) (tell why you are using the statistic

you have chosen) is it a strong relationship?

Graphics assessment of graphics (2-3 sentences) What is the graph telling you?

o Basic idea of what it is demonstrating

R help

Anything that is at the end of arrow <- is the new name

For example: tom <- read.spss)”/users

Bill <- read.spss

Step 1: Attach (Tom)

Step 2: Names (Tom)

Step 3: Is.factor(e033) asking if an object is a factor or not (in this asking if tom is a factor)

Step 4: Lftrght <- as.numeric(e033) changing data into numeric

False= good thing b/c it means it is simpler to work with.

Step 5: Is.factor(lftrght)

Step 6: Lftrght <- lftrght -5

Lftrght

Creating table

LR tab<- table(lftrght)

LRtab

LRfreq <- c(1210, 707, 1394 etc…)

Creating a Mosaic Plot

LR3cat <= lftrght (recoding left right into LR3cat)

LR3cat[lftrght>0 & lftrght<4] <-0

LR3cat[lftrght>3 & lftrght<8] <-1

LR3cat[lftrght>7 & lftrght<11] <-2

Quantitative Measurement: How indicators fit together

Indexes

Recall that in first week, create measures that could be constructed using more than one

indicator of a given concept.

When we use multiple indicators in order to measure a concept, we call the resulting concept an

“index”

4 major steps in creating index:

1) Find a set of indicators that are closely related to underlying latent variable that you are

interested in measuring.

2) Recode indicators so that they have same direction and range.

3) Test indicators that you have recoded to see how well they fit together.

4) Once you have identified a set of indicators that are a good fit for the underlying latent concept,

combine them into a single index.

Step one: finding indicators

Generally the most difficult.

Combing through data set that you are interested in using in order to find suitable indicators of

the key concepts you are looking for.

Step two: recoding indicators

Direction and range are concerns (Range has to be 0 and 1)

Directionality of indicators

We want to make sure that each of our indicators (higher means morally traditional and lower

means less morally traditional)

What does same direction and range mean?

Same directionality conceive of your latent variable in terms of one end of the spectrum of

views that you intend to consider.

o E.g. moral traditionalism

o What’s the opposite of moral traditionalism?

Morally liberal? Morally progressive? Morally corrupt?

Then recode each of your variables so that the higher values of you indicators represent this end

of the spectrum of views that you are intending to measure.

o Do you think abortion is murder? This is on moral traditionalism scale.

Strongly agree-> high value

o DO you think women have the right to abortion?

Strongly disagreelow value