Re: Normality in Factor Analysis
Robert Ehrlich [EMAIL PROTECTED] wrote in message [EMAIL PROTECTED]">news:[EMAIL PROTECTED]... Calculation of eigenvalues and eigenvalues requires no assumption. However evaluation of the results IMHO implicitly assumes at least a unimodal distribution and reasonably homogeneous variance for the same reasons as ANOVA or regression. So think of th consequencesof calculating means and variances of a strongly bimodal distribution where no sample ocurrs near the mean and all samples are tens of standard devatiations from the mean. The largest number of standard deviations all data can be from the mean is 1. To get some data further away than that, some of it has to be less than 1 s.d. from the mean. Glen = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Normality in Factor Analysis
Calculation of eigenvalues and eigenvalues requires no assumption. However evaluation of the results IMHO implicitly assumes at least a unimodal distribution and reasonably homogeneous variance for the same reasons as ANOVA or regression. So think of th consequencesof calculating means and variances of a strongly bimodal distribution where no sample ocurrs near the mean and all samples are tens of standard devatiations from the mean. Hi, I have a question regarding factor analysis: Is normality an important precondition for using factor analysis? If no, are there any books that justify this. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Maximum likelihood Was: Re: Factor Analysis
In article [EMAIL PROTECTED], Ken Reed [EMAIL PROTECTED] wrote: It's not really possible to explain this in lay person's terms. The difference between principal factor analysis and common factor analysis is roughly that PCA uses raw scores, whereas factor analysis uses scores predicted from the other variables and does not include the residuals. That's as close to lay terms as I can get. I have never heard a simple explanation of maximum likelihood estimation, but -- MLE compares the observed covariance matrix with a covariance matrix predicted by probability theory and uses that information to estimate factor loadings etc that would 'fit' a normal (multivariate) distribution. MLE factor analysis is commonly used in structural equation modelling, hence Tracey Continelli's conflation of it with SEM. This is not correct though. I'd love to hear simple explanation of MLE! MLE is triviality itself, if you do not make any attempt to state HOW it is to be carried out. For each possible value X of the observation, and each state of nature \theta, there is a probability (or density with respect to some base measure) P(X | \theta). There is no assumption that X is a single real number; it can be anything; the same holds about \theta. What MLE does is to choose the \theta which makes P(X | \theta) as large as possible. That is all there is to it. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Normality in Factor Analysis
In article 9gg7ht$qa3$[EMAIL PROTECTED], haytham siala [EMAIL PROTECTED] wrote: Hi, I have a question regarding factor analysis: Is normality an important precondition for using factor analysis? If no, are there any books that justify this. Factor analysis is quite robust against non-normality. The essential factor structure is little affected by it at all, although the representation may get somewhat sensitive if data-dependent normalizations are used, such as using correlations rather than covariances, or forcing normalization on the covariance matrix of the factors. Some of this is in my paper with Anderson in the Proceedings of the Third Berkeley Symposium. The result on the asymptotic distribution, not at all difficult to derive, is in one of my abstracts in _Annals of Mathematical Statistics_, 1955. It is basically this: Suppose the factor model is x = \Lambda f + s, f the common factors and s the specific factors. Further suppose that f and s, and also the elements of s, are uncorrelated, and there is adequate normalization and smooth identification of the model by the elements of \Lambda alone. Now estimate \Lambda, M, the covariance matrix of f, and S, the diagonal covariance matrix of s. Assuming the usual assumptions for asymptotic normality of the sample covariances of the elements of f with s, and of the pairs of different elements of s, the asymptotic distribution of the estimates of \Lambda and the SAMPLE values of M and S from their actual values will have the expected asymptotic joint normal distribution. This makes no assumption about the distribution of M and S about their expected values, which is the main place were there is an effect of normality. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Factor Analysis
It's not really possible to explain this in lay person's terms. The difference between principal factor analysis and common factor analysis is roughly that PCA uses raw scores, whereas factor analysis uses scores predicted from the other variables and does not include the residuals. That's as close to lay terms as I can get. I have never heard a simple explanation of maximum likelihood estimation, but -- MLE compares the observed covariance matrix with a covariance matrix predicted by probability theory and uses that information to estimate factor loadings etc that would 'fit' a normal (multivariate) distribution. MLE factor analysis is commonly used in structural equation modelling, hence Tracey Continelli's conflation of it with SEM. This is not correct though. I'd love to hear simple explanation of MLE! From: [EMAIL PROTECTED] (Tracey Continelli) Organization: http://groups.google.com/ Newsgroups: sci.stat.consult,sci.stat.edu,sci.stat.math Date: 15 Jun 2001 20:26:48 -0700 Subject: Re: Factor Analysis Hi there, would someone please explain in lay person's terms the difference betwn. principal components, commom factors, and maximum likelihood estimation procedures for factor analyses? Should I expect my factors obtained through maximum likelihood estimation tobe highly correlated? Why? When should I use a Maximum likelihood estimation procedure, and when should I not use it? Thanks. Rita [EMAIL PROTECTED] Unlike the other methods, maximum likelihood allows you to estimate the entire structural model *simultaneously* [i.e., the effects of every independent variable upon every dependent variable in your model]. Most other methods only permit you to estimate the model in pieces, i.e., as a series of regressions whereby you regress every dependent variable upon every independent variable that has an arrow directly pointing to it. Moreover, maximum likelihood actually provides a statistical test of significance, unlike many other methods which only provide generally accepted cut-off points but not an actual test of statistical significance. There are very few cases in which I would use anything except a maximum likelihood approach, which you can use in either LISREL or if you use SPSS you can add on the module AMOS which will do this as well. Tracey = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Factor Analysis
Dear Haytham, other issue concern with a measure of the latent construct is the unidimensionality. Hair et alli(1998): unidimensionality is an assumption underlying the calculation of reliability and is demonstraded when indicators of a construct have acceptable fit on a single-factor(one-dimensional) model.(...) The use of reliability measures, such Cronbach´s alpha, does not ensure unidimensionality but instead assumes it exists. The researcher is encouraged to perform unidimensionality tests on all multiple-indicator constructs before assessing their reliability. This reference is very important: Gerbing, David W., Anderson, James C. An updated paadigm for scale development incorporating unidimensionality and its assesment. Best regards, Alexandre Moura. P.S. Please accept my apologies for my English mistakes. - Original Message - From: haytham siala [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Friday, June 15, 2001 5:40 PM Subject: Factor Analysis Hi, I will appreciate if someone can help me with this question: if factors extracted from a factor analysis were found to be reliable (using an internal consistency test like a Cronbach alpha), can they be used to represent a measure of the latent construct? If yes, are there any references or books that justify this technique? = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ = = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Factor Analysis
The complete reference: Gerbing, David W., Anderson, James C. An updated paradigm for scale development incorporating unidimensionality and its assesment. Journal of Marketing Research. Vol. XXV (May 1988). Alexandre Moura. - Original Message - From: Alexandre Moura [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Saturday, June 16, 2001 9:26 AM Subject: Re: Factor Analysis Dear Haytham, other issue concern with a measure of the latent construct is the unidimensionality. Hair et alli(1998): unidimensionality is an assumption underlying the calculation of reliability and is demonstraded when indicators of a construct have acceptable fit on a single-factor(one-dimensional) model.(...) The use of reliability measures, such Cronbach´s alpha, does not ensure unidimensionality but instead assumes it exists. The researcher is encouraged to perform unidimensionality tests on all multiple-indicator constructs before assessing their reliability. This reference is very important: Gerbing, David W., Anderson, James C. An updated paadigm for scale development incorporating unidimensionality and its assesment. Best regards, Alexandre Moura. P.S. Please accept my apologies for my English mistakes. - Original Message - From: haytham siala [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Friday, June 15, 2001 5:40 PM Subject: Factor Analysis Hi, I will appreciate if someone can help me with this question: if factors extracted from a factor analysis were found to be reliable (using an internal consistency test like a Cronbach alpha), can they be used to represent a measure of the latent construct? If yes, are there any references or books that justify this technique? = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ = = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ = = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Normality in Factor Analysis
Hi, I have a question regarding factor analysis: Is normality an important precondition for using factor analysis? If no, are there any books that justify this. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Normality in Factor Analysis
In sci.stat.consult haytham siala [EMAIL PROTECTED] wrote: I have a question regarding factor analysis: Is normality an important precondition for using factor analysis? It's necessary for testing hypotheses about factors extracted by Joreskog's maximum-likelihood method. Otherwise, no. If no, are there any books that justify this. Any book on factor analysis or multivariate statistics in general. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Factor Analysis
Hi there, would someone please explain in lay person's terms the difference betwn. principal components, commom factors, and maximum likelihood estimation procedures for factor analyses? Should I expect my factors obtained through maximum likelihood estimation tobe highly correlated? Why? When should I use a Maximum likelihood estimation procedure, and when should I not use it? Thanks. Rita [EMAIL PROTECTED] Unlike the other methods, maximum likelihood allows you to estimate the entire structural model *simultaneously* [i.e., the effects of every independent variable upon every dependent variable in your model]. Most other methods only permit you to estimate the model in pieces, i.e., as a series of regressions whereby you regress every dependent variable upon every independent variable that has an arrow directly pointing to it. Moreover, maximum likelihood actually provides a statistical test of significance, unlike many other methods which only provide generally accepted cut-off points but not an actual test of statistical significance. There are very few cases in which I would use anything except a maximum likelihood approach, which you can use in either LISREL or if you use SPSS you can add on the module AMOS which will do this as well. Tracey = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Factor Analysis
_Psychometric Theory_, by Jum Nunnally to name one. haytham siala wrote: Hi, I will appreciate if someone can help me with this question: if factors extracted from a factor analysis were found to be reliable (using an internal consistency test like a Cronbach alpha), can they be used to represent a measure of the latent construct? If yes, are there any references or books that justify this technique? -- Timothy Victor [EMAIL PROTECTED] Policy Research, Evaluation, and Measurement Graduate School of Education University of Pennsylvania = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: factor analysis of dichotomous variables
A list of such programs and discussion can be found at: http://ourworld.compuserve.com/homepages/jsuebersax/binary.htm The results of Knol Berger (1991) and Parry MacArdle (1991) (see above web page for citations) suggest that there is not much difference in results between the Muthen method and the simpler method of factoring tetrachoric correlations. For additional information (including examples using PRELIS/LISREL and SAS) on factoring tetrachorics, see http://ourworld.compuserve.com/homepages/jsuebersax/irt.htm Hope this helps. John Uebersax = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
PCA and factor analysis: when to use which
What is the basis for deciding when to use principal components analysis and when to use factor analysis. Could anyone describe a problem that illustrates the difference? = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
