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
In article <[EMAIL PROTECTED]>, Robert Ehrlich <[EMAIL PROTECTED]> wrote: >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. Unimodality is not a concern at all. Asymptotic distributions of moments only involve moments, and factor analysis is carried out on sample moments. One cannot have all observations "tens of standard deviations from the mean". The Chebyshev inequality limits how large the tails can be. There are problems if the covariance matrix varies from observation to observation, even with the same sample structure. See my previous posting on what can be done with weak assumptions. >> 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. -- 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
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/ =
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: Normality in Factor Analysis
I have checked some of the books but I could not find this statment (for e.g. using multivariate statistics (Tabachnik 1996), Latent variable models (Loehlin 1998), Easy guide to factor analysis (Kline 1994)). Can you please give me a examples of references as I reallly need a reference because I have already conducted a factor analysis on sample of data containing some non-normal variables . - Original Message - From: "Eric Bohlman" <[EMAIL PROTECTED]> Newsgroups: sci.stat.consult,sci.stat.edu,sci.stat.math Sent: Sunday, June 17, 2001 2:08 AM Subject: 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. > "Eric Bohlman" <[EMAIL PROTECTED]> wrote in message 9ggvug$451$[EMAIL PROTECTED]">news:9ggvug$451$[EMAIL PROTECTED]... > 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: 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/ =
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/ =
