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Factor Analysis: A Short Introduction, Part 2–Rotations

September 24th, 2012 by

by Maike Rahn, PhD

Rotations

An important feature of factor analysis is that the axes of the factors can be rotated within the multidimensional variable space. What does that mean?

Here is, in simple terms, what a factor analysis program does while determining the best fit between the variables and the latent factors: (more…)


Factor Analysis: A Short Introduction, Part 1

September 10th, 2012 by

Why use factor analysis?

Factor analysis is a useful tool for investigating variable relationships for complex concepts such as socioeconomic status, dietary patterns, or psychological scales.

It allows researchers to investigate concepts they cannot measure directly. It does this by using a large number of variables to esimate a few interpretable underlying factors.

What is a factor?

The key concept of factor analysis is that multiple observed variables have similar patterns of responses because they are all associated with a latent variable (i.e. not directly measured). (more…)


Stratified Sampling for Oversampling Small Sub-Populations

June 11th, 2012 by

by Ritu Narayan

Sampling is a critical issue in any research study design. Most of us have grappled with balancing costs, time and of course, statistical power when deciding our sampling strategies.

How do we know when to go for a simple random sample or to go for stratification or for clustering? Let’s talk about stratified sampling here and one research scenario when it is useful.

One Scenario for Stratified Sampling

Suppose you are studying minority groups and their behavior, say Yiddish speakers in the U.S. and their voting.  Yiddish speakers are a small subset of the US population, just .6%. (more…)


How to do a Chi-square test when you only have proportions and denominators

March 18th, 2011 by

by Annette Gerritsen, Ph.D.

In an earlier article I discussed how to do a cross-tabulation in SPSS. But what if you do not have a data set with the values of the two variables of interest?

For example, if you do a critical appraisal of a published study and only have proportions and denominators.

In this article it will be demonstrated how SPSS can come up with a cross table and do a Chi-square test in both situations. And you will see that the results are exactly the same.

‘Normal’ dataset

If you want to test if there is an association between two nominal variables, you do a Chi-square test.

In SPSS you just indicate that one variable (the independent one) should come in the row, (more…)


How to Set up Censored Data for Event History Analysis

November 12th, 2010 by

Censored data are inherent in any analysis, like Event History or Survival Analysis, in which the outcome measures the Time to Event TTE. Censoring occurs when the event doesn’t occur for an observed individual during the time we observe them.

Despite the name, the event of “survival” could be any categorical event that you would like to describe the mean or median TTE.  To take the censoring into account, though, you need to make sure your data are set up correctly.

Here is a simple example, for a data set that measures days after surgery until an (more…)


Censoring in Time-to-Event Analysis

November 9th, 2010 by

Time to event analyses (aka, Survival Analysis and Event History Analysis) are used often within medical, sales and epidemiological research. Some examples of time-to-event analysis are measuring the median time to death after being diagnosed with a heart condition, comparing male and female time to purchase after being given a coupon and estimating time to infection after exposure to a disease.

Survival time has two components that must be clearly defined: a beginning point and an endpoint that is reached either when the event occurs or when the follow-up time has ended.

One basic concept needed to understand time-to-event (TTE) analysis is censoring.

In simple TTE, you should have two types of observations:

1. The event occurred, and we are able to measure when it occurred OR

2. The event did NOT occur during the time we observed the individual, and we only know the total number of days in which it didn’t occur. (CENSORED).

Again you have two groups, one where the time-to-event is known exactly and one where it is not. The latter group is only known to have a certain amount of time where the event of interest did not occur. We don’t know if it would have occurred had we observed the individual longer. But knowing that it didn’t occur for so long tells us something about the risk of the envent for that person.

For example, let the time-to-event be a person’s age at onset of cancer. If you stop following someone after age 65, you may know that the person did NOT have cancer at age 65, but you do not have any information after that age.

You know that their age of getting cancer is greater than 65. But you do not know if they will never get cancer or if they’ll get it at age 66, only that they have a “survival” time greater than 65 years. They are censored because we did not gather information on that subject after age 65.

So one cause of censoring is merely that we can’t follow people forever.  At some point you have to end your study, and not all people will have experienced the event.

But another common cause is that people are lost to follow-up during a study. This is called random censoring. It occurs when follow-up ends for reasons that are not under control of the investigator.

In survival analysis, censored observations contribute to the total number at risk up to the time that they ceased to be followed.  One advantage here is that the length of time that an individual is followed does not have to be equal for everyone. All observations could have different amounts of follow-up time, and the analysis can take that into account.

Allison, P. D. (1995). Survival Analysis Using SAS. Cary, NC: SAS Institute Inc.

Hosmer, D. W. (2008). Applied Survival Analysis (2nd ed.). Hoboken, NJ: John Wiley & Sons, Inc.