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I'm interested in getting some books about multivariate analysis, and need your recommendations. Free books are always welcome, but if you know about some great non-free MVA book, please, state it.

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To what extent do you want: (a) mathematical rigour; (b) applications in particular software (e.g., R, SPSS, SAS, etc.); (c) domain-specific applications? –  Jeromy Anglim Aug 29 '10 at 13:12
    
Jeromy, allow me to take all of these with one blow: I'm a psychology student. And I reckon you're familiar with required statistical background... So there... =) (I'm good with R and SPSS... but R has a greater priority) –  aL3xa Aug 29 '10 at 15:26
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10 Answers

Off the top of my head, I would say that the following general purpose books are rather interesting as a first start:

There is also many applied textbook, like

It is difficult to suggest you specific books as there are many ones that are domain-specific (e.g. social sciences, machine learning, categorical data, biomedical data).

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why the Tinsley book? No reviews on Amazon suggests it ain't a big seller or particularly good. –  Neil McGuigan Aug 31 '10 at 23:18
    
Just because it is the only book I know which combines exploratory MV analysis, statistical modeling, and psychometrics. Maybe not the best one actually, but interesting on its own. –  chl Sep 4 '10 at 16:59
    
I think of it as one of the 4 or 5 most important books I own. –  rolando2 Feb 15 '12 at 23:12
    
Can you somehow comment on the exercises of these books? I want to do some exercises from a graduate level, mathematics-biased text book to enhance. Thank you. –  ziyuang Aug 12 '13 at 12:15
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Almost the same question was asked recently on the ISOSTAT listserver (frequented by college professors):

If you had a strong undergraduate student who was interested in learning about various multivariate methods (e.g. PCA, MANOVA, discriminant analysis, ...) is there a good, accessible book you might recommend she/he purchase?

Here are the responses:

  • Perhaps "Applied Multivariate Data Analysis", 2nd edition, by Everitt, B. and Dunn, G. (2001), published by Arnold. [Roger Johnson]

  • Rencher's Methods of Multivariate Analysis is a great resource. I think a strong undergraduate student could grasp the material. [Philip Yates]. I'm fond of Rencher's approach. He offers good intuition and examples. But the matrix algebra can get pretty thick; I'm not sure "accessible" is an adjective I'd use. Nevertheless, I've taught undergrads successfully with his book. His second edition is a good improvement over the first. [Paul Velleman]

  • Applied Multivariate Statistics by Johnson and Wichern. [Brad Hartlaub]

  • I haven't done much with it, but I do like the idea of using modern techniques and modern data sets: Modern Multivariate Statistical Techniques by Alan Julian Izenman. (I own the book, it has the topics you are looking for, and the text seems accessible.) [Johanna Hardin]

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(+1) I like the first, and especially the last one (pretty much the same as the Elements of Statistical Learning, by Hastie and coll., but with other examples and a discussion of biplots and correspondence analysis). –  chl Mar 22 '11 at 17:31
    
+1 for mentioning Rencher's book. It's fantastic, and also has a chapter for matrix algebra and required background maths. –  aL3xa Mar 22 '11 at 17:43
    
+1 for Everitt & Dunn, we used it for a joint undergrad/grad class and it was quite good, nice and direct. –  JMS May 29 '11 at 21:58
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Here are some of my books on that field (in alphabetical order).

  • AFIFI, A., CLARK, V. Computer-Aided Multivariate Analysis. CHAPMAN & HALL, 2000
  • AGRESTI, A. Categorical Data Analysis. WILEY, 2002
  • HAIR, Multivariate Data Analysis. 6th Ed.
  • ΗÄRDLE, W., SIMAR, L. Applied Multivariate Statistical Analysis. SPRINGER, 2007.
  • HARLOW, L. The Essence of Multivariate Thinking. LAWRENCE ERLBAUM ASSOCIATES, INC., 2005
  • GELMAN, A., HILL, J. Data Analysis Using Regression and Multilevel/Hierarchical Models. CAMBRIDGE UNIVERSITY PRESS, 2007.
  • IZENMAN, A. J. Modern Multivariate Statistical Techniques. SPRINGER, 2008
  • RENCHER, A. Methods of Multivariate analysis. SECOND ED., WILEY-INTERSCIENCE, 2007
  • TABACHNICK B., FIDELL, L. Using Multivariate Statistics. 5th Ed. Pearson Education. Inc, 2007.
  • TIMM, N. Applied Multivariate Analysis. SPRINGER, 2002
  • YANG, K., TREWN, J. Multivariate Statistical Methods in Quality Management. MCGRAW-HILL, 2004
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do you recommend to read all of them ? :) –  robin girard Aug 29 '10 at 10:41
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In Psychology the Tabachnik & Fidell Book has a pretty good reputation. It is very understandable and applied and not too mathematic. However, examples are only in SPSS or SAS (no R!). But if your problem is covered in there, you will definitely solve it with the book. I recommend it as a good starting point. I don't like the Hair book (same level as Tabachnik & Fidell, but worse). And you gotta LOVE the Gelman. However, it is more complicated. –  Henrik Aug 29 '10 at 12:00
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HAIR et al is good if you don't like math and you want a step by step process. It's popular in management and business schools. If you can handle math, Hair et al can seem verbose. Tabachnick and Fidell is popular in psychology. It's clearly written and does contain some mathematics. However, if you want a rigorous mathematical treatment, I'd look for an additional book to complement it. –  Jeromy Anglim Aug 29 '10 at 13:09
    
Thanks for giving accent to statistics in psychology. –  aL3xa Aug 29 '10 at 15:31
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JOHNSON R., WICHERN D., Applied Multivariate Statistical Analysis, is what we used in our undergraduate Multivariate class at UC Davis, and it does a pretty good job (though it's a bit pricey).

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Hands down best basic text on multivariate regression is (still) Cohen, J., Cohen, P., West, S.G. & Aiken, L.S. Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences, (L. Erlbaum Associates, Mahwah, N.J., 2003).

Cohen made his name in statistics yet was a psychologist; still if you want social psychology-focused treatment of multivariate, one not limited to multivariate regression (although it definitely favors it over ANOVA & MANOVA, which ought to be banned by some sort of Intellectual Human Rights Commission), then your best bet is Judd, C.M., McClelland, G.H. & Ryan, C.S. Data analysis : a model comparison approach, (Routledge/Taylor and Francis, New York, NY, 2008). Judd also has a very very good chapter on multivariate regression in Judd, C.M. Everyday Data Analysis in Social Psychology: Comparisons of Linear Models. in Handbook of research methods in social and personality psychology (eds. Reis, H.T. & Judd, C.M.) 370-392 (Cambridge University Press, New York, 2000).

I agree that Gelman, A. & Hill, J. Data Analysis Using Regression and Multilevel/Hierarchical Models, (Cambridge University Press, Cambridge ; New York, 2007), is amazing, but it is really more geared to someone already comfortable w/ basics of multivariate regression--it's primarily about multilevel modeling. Also is focused on observational study methodology--not experimental (Judd is best for that; Cohen okay too.

If you want something on interactions in multivariate -- which you likely will if you are using experimental methods -- then best two texts are Aiken, L.S., West, S.G. & Reno, R.R. Multiple Regression: Testing and Interpreting Interactions, (Sage Publications, Newbury Park, Calif., 1991) & Jaccard, J. & Turrisi, R. Interaction Effects in Multiple Regression, (Sage Publications, Thousand Oaks, Calif., 2003). (Both Cohen & Cohen & Judd do treat this topic, though.)

On "free" side, you probably know about http://faculty.chass.ncsu.edu/garson/PA765/statnote.htm

Last bit of advice: Never ever split your continuous variables!!! It's amazing how many social psychologists, used to ANOVA, still do this even as they make use of multivariate techniques such as regression analysis!

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Analyzing Multivariate Data by James Lattin, J Douglas Carroll and Paul E Green.

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Tabachnick is the most cited on Google Scholar

Hair (6th ed) has the most ratings (with a score above 4.5) on Amazon

I recommend Hair, as I've read it, and it is written in plain language.

If you are a student or staff at a university, then I would see if your school has an account with SpringerLink, as the Hardle book is on there for free.

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I actually found Tabachnick rather unclear, even for subjects i knew quite a bit about. The introductory stuff on univariate stats and data cleaning was very good though –  richiemorrisroe Mar 22 '11 at 22:09
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Hastie, T., Tibshirani, R. and Friedman, J.: "The Elements of Statistical Learning: Data Mining, Inference, and Prediction.", Springer (book home page)

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If you look at Paul Hewison's webpage, you can find his free book on Multivariate Statistics and R. Another free book is by Wolfgang Hardle and Leopold Simar. I have been working my way through Johnson and Wichern, a book that has been used in the US for over twenty years; you will have to buy this book.

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"An Introduction to Multivariate Statistical Analysis" Third edition by T. W. Anderson . Wiley series in Probability and Statistics.

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How do you think about the problems within? I happen to own this and want to do some exercises for enhancement. –  ziyuang Aug 12 '13 at 12:06
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