I thought factor analysis can proceed if some of the correlations are

negative.

Hector

-----Mensaje original-----

De: SPSSX(r) Discussion [mailto:

[hidden email]] En nombre de

Anthony Babinec

Enviado el: Thursday, August 03, 2006 11:24 AM

Para:

[hidden email]
Asunto: Re: factor analyzing the Tetrachoric correlations

Here are a few points:

For dichotomous indicators, the tetrachoric correlation

is NOT equivalent to the pearson correlation computed on

the dichotomies.

The matrix of tetrachoric correlations is not necessarily

positive definite, so situations can arise in FACTOR where

you get those error messages about negative eigenvalues

and noninvertibility.

There's a good current paper by Sara Finney and Christine

DiStefano entitled "Nonnormal and Categorical Data

in Structural Equation Modeling" that reviews current

approaches in software and makes recommendations. Factor analysis

and regression are of course subsumed in SEM. The paper is in

"Structural Equation Modeling: A Second Course" edited

by Gregory Hancock and Ralph Mueller.

-----Original Message-----

From: SPSSX(r) Discussion [mailto:

[hidden email]] On Behalf Of

Dale Glaser

Sent: Wednesday, August 02, 2006 9:23 PM

To:

[hidden email]
Subject: Re: factor analyzing the Tetrachoric correlations

..and to add to what Richard said, I don't have the Mplus manual in front of

me, but there is a different WLS-type of estimator that Mplus uses for

binary factor analysis that does not correspond to SPSS...I ran a binary EFA

a few weeks ago in both Mplus and SPSS (importing the tetrachorics) and

there was quite a difference in the magnitude of the loadings.....I am

assuming that is due to the estimator involved.........

Dale

Richard Ristow <

[hidden email]> wrote:

At 08:45 PM 7/31/2006, Dogan, Enis wrote:

>I am factor analyzing a set of 42 dichotomously scored test items. I

>calculated the Tetrachoric correlations; so my input file is a

>correlation matrix.

Hector has replied very succinctly. Scanning, I found a more extended

note he'd written on the same subject. It seems excellent, and I'm

reproducing it below. Hector, I hope you don't mind.

I add one rough-and-ready point. It is not visible in the correlation

matrix, but a dichotomous observation always conveys less information

than does a continuous one. I can't think of a way to quantify how much

less. It depends on factors including the relative proportion of 0's

and 1's in the dichotomous variable, and the signal-to-noise ratio of

the continuous one. I'll throw out, off the cuff, that a dichotomous

variable might be about 1/5 as informative as a continous one.

Pending the opinions of those much better qualified (Hector, Marta,

...), be very careful of your sample size. I don't know the recommended

ratio of cases to variables for FA, but whatever it is, it must be

increased for FA of dichotomous variables. Quintuple? Maybe.

But, Hector's earlier response: At 01:24 PM 12/15/2004, Hector Maletta

wrote (subject "Re: factor analysis of tetrachloric correlations"):

>As I see it, the selection of a method for extraction or rotation is

>not related to the kind of correlation you have. In fact, so called

>tetrachoric correlations are equivalent to Pearson product-moment

>correlations for binary variables coded 0,1. The choice of extraction

>and rotation depends on the purpose of your analysis and the

>underlying theoretical model. For instance, the Principal Components

>extraction method would try to locate a major underlying factor

>explaining as much commolatity as possible, while the Principal Axis

>method would look for several possible independent (orthogonal)

>factors explaining different parts of the commonalities.

>

>Historically, the PC method was developed by Spearmann when looking

>for a General Intelligence factor underlying all intelligence tests,

>while the PA method was introduced by Thurstone to prove his point

>that there are several dimensions of intelligence and not just one. As

>it turns out, factors identified by factor analysis are but analytical

>constructs, not real objects, and by careful choice of method you can

>obtain a variety of solutions that reduce the dimensionality of your

>variable-space to a factor space defined by one or many factors,

>orthogonal or correlated, without proving anything about the validity

>of each solution: it only proves that various different mathematical

>models are consistent with the data.

Dale Glaser, Ph.D.

Principal--Glaser Consulting

Lecturer--SDSU/USD/CSUSM/AIU

4003 Goldfinch St, Suite G

San Diego, CA 92103

phone: 619-220-0602

fax: 619-220-0412

email:

[hidden email]
website: www.glaserconsult.com