Measurement, Scaling, and Dimensional Analysis
Summer 2013
Jacoby/Armstrong
ALTERNATING LEAST SQUARES OPTIMAL
SCALING REGRESSION ANALYSIS
Part 1, Data: The ALSOS analysis will use data from the 1992 CPS National Election Study. The data are
contained with
Measurement, Scaling, and Dimensional Analysis
Summer 2013
UNIDIMENSIONAL UNFOLDING EXAMPLE
Occupations (and abbreviations):
Business executive (B)
Consultant (C)
Lawyer (L)
Professor (P)
Sales representative (S)
Preference Orders among Occupations Given
Measurement, Scaling, and Dimensional Analysis
Jacoby/Armstrong
Summer 2013
UNFOLDING ANALYSIS WITH DICHOTOMOUS ITEMS
In a study of state governmental priorities, a sample of representatives from state governors offices were
asked about the importance of
Measurement, Scaling, and Dimensional Analysis
Summer 2013
Jacoby/Armstrong
UNIDIMENSIONAL UNFOLDING WITH SPSS
Note that the screen shots in this handout are taken from SPSS 16.0. More recent versions of the software
look a bit different, but the steps in
Measurement, Scaling and Dimensional Analysis
Handout 1: Simple SVD
ICPSR Summer Program
2013
Here is a trivially simple example of an SVD, but it highlights some interesting properties.
First, I want to make some data that has certain properties. I want
Measurement, Scaling and Dimensional Analysis
Handout 2: Singular Value Decomposition
ICPSR Summer Program
2013
Here is a slightly more complicated example, but one that continues to highlight some
important features of the SVD, but with more real-like da
Measurement, Scaling and Dimensional Analysis
Handout 3: SVD with Real Data
ICPSR Summer Program
2013
Now that we have an intuition for what the SVD does, lets look at it using some real
data. Here, we are using data from Arthur Banks Cross-National Time-
Measurement, Scaling and Dimensional Analysis
Handout 4: Biplots
ICPSR Summer Program
2013
We can use our previous SVD solution in Handout 2 to discuss the rst biplot. Remember,
we can nd coordinates in the following way:
>
>
+
>
>
set.seed(123)
sig <- ma
Measurement, Scaling and Dimensional Analysis
Handout 5: Biplots with Banks Data
ICPSR Summer Program
2013
To make a biplot of the Banks data we used in Handout 3, we rst need to read in the
data and compute the SVD.
>
>
>
+
+
>
>
>
>
>
>
library(foreign)
Measurement, Scaling and Dimensional Analysis
Handout: Principal Components with Banks Data
ICPSR Summer Program
2013
We can use the Banks data to perform a Principal Components Analysis. First, lets load
the data and do a bit of investigating.
> library(
Measurement, Scaling and Dimensional Analysis
Handout: Principal Components: Democracy
ICPSR Summer Program
2013
Another example, close to my own research, is using democracy data. Lets take a look
at the polity data.
Table
Variable
ccode
scode
country
de
Measurement, Scaling and Dimensional Analysis
Handout: Control Variables and PCA
ICPSR Summer Program
2013
One situation where PCA can be a useful technique in its own right is with control
variables. Consider the problem of controlling for economic devel
Measurement, Scaling and Dimensional Analysis
Handout: Optimal Linear Transformations in R
ICPSR Summer Program
2013
Principal components (and factor analysis, for that matter), capitalize on linear relationships in the data. If the relationships are non-
Measurement, Scaling and Dimensional Analysis
Handout: Factor Analysis - Mathematical Results
ICPSR Summer Program
2013
There are a number of useful mathematical results that help us think about the nature
of the Common Factor Model and will ultimately he
Measurement, Scaling and Dimensional Analysis
Handout: Factor Analysis
ICPSR Summer Program
2013
Were using data from the 2008 American National Election Study (anes2008ft.csv)
which asks a number of feeling thermometer questions. Specically, we are using
Measurement, Scaling and Dimensional Analysis
Handout: Factor Analysis - Confounding Variables
ICPSR Summer Program
2013
We talked some in class about the possibility of other confounding or omitted variables,
and I wanted to provide you some guidance on
Measurement, Scaling, and Dimensional Analysis
Jacoby/Armstrong
Summer 2013
TRANSFORMING DISTANCES INTO SCALAR PRODUCTS
The square, symmetric matrix, , contains dissimilarities among a set of k objects. So, for example,
entry ij represents the dissimilari
Measurement, Scaling and Dimensional Analysis
Handout: Factor Analysis - R and Stata
1
ICPSR Summer Program
2013
Data
To demonstrate, Ill use the WVS data. To remind, the variables included are:
Variable
age
country
educ
employment
ethnic
just abortion
ju
Measurement, Scaling, and Dimensional Analysis
Summer 2013
Jacoby/Armstrong
METRIC MULTIDIMENSIONAL SCALING
Raw Input Data ( Matrix of Dissimilarities): Driving Distances Between Ten American Cities (in
Thousands of Miles).
0
0.587
1.212
0.701
1.936
0.604
Measurement, Scaling, and Dimensional Analysis
Summer 2013
Jacoby/Armstrong
METRIC MDS IN R
This handout shows the contents of an R session that carries out a metric multidimensional scaling analysis
of the driving distances between ten U.S. cities. The a
Measurement, Scaling, and Dimensional Analysis
Jacoby/Armstrong
Summer 2013
MULTIDIMENSIONAL SCALING IN STATA, I
This handout shows the STATA log from a session that performs a metric multidimensional scaling analysis
of the data on intercity distances. S
Measurement, Scaling, and Dimensional Analysis
Summer 2013
Jacoby/Armstrong
PROFILE DISSIMILARITIES AMONG TEN AMERICAN CITIES
Table 1: Socioeconomic characteristics of ten American cities.
Climate,
Terrain
Atlanta
Chicago
Denver
Houston
LA
Miami
NYC
SF
Se
Measurement, Scaling, and Dimensional Analysis
Summer 2013
Jacoby/Armstrong
A SIMPLE EXAMPLE OF NONMETRIC
MULTIDIMENSIONAL SCALING
Matrix 1: Hypothetical data matrix, showing dissimilarities between four political candidates. Cell
entries show rank order
Measurement, Scaling, and Dimensional Analysis
Jacoby/Armstrong
Summer 2013
NONMETRIC MDS IN R
This handout shows the listing from an R session that performs a nonmetric multidimensional
scaling analysis of dissimilarities among 13 prominent political gur
Measurement, Scaling, and Dimensional Analysis
Summer 2013
Jacoby/Armstrong
NONMETRIC MDS OF 2004 PRESIDENTIAL CANDIDATES
How did citizens evaluate the political landscape during the 2004 American presidential election campaign?
In other words, what evalu