Re: Regression with repeated measures
On Wed, 28 Feb 2001, Mike Granaas wrote in part (and 2 paragraphs of descriptive prose quoted at the end): ... is there some method that will allow him to get the prediction equation he wants? Probably the best approach is the multilevel (aka hierarchical) modelling advocated by previous respondents. Possible problems with that approach: (1) you'll need purpose-built software, which may not be conveniently available at USD; (2) the user is usually required (as I rather vaguely recall from a brush with Goldstein's ML3 a decade ago) to specify which (co)variances are to be estimated in the model, both within and between levels, and if your student isn't up to this degree of technical skill, (s)he may not have a clue as to what the output will be trying to say. For a conceptually simpler, if less rigorous, approach, the problem could be addressed as an analysis of covariance (to use the now old-fashioned language), using the intended predictor as the covariate and the 10 (or whatever number of) trials for each S as a blocking variable (as in randomized blocks in ANOVA). This would at least bleed off (so to write) some of the excess number of degrees of freedom; especially if one also modelled interaction between predictor and blocking variable (which might well require a GLM program, rather than an ANCOVA program), as in testing homogeneity of regression. The blocking variable itself might be interpretable (if one were interested) as an (idiosyncratic?) amalgam of practice/learning and fatigue. -- Don. -- Donald F. Burrill[EMAIL PROTECTED] 348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED] MSC #29, Plymouth, NH 03264 (603) 535-2597 Department of Mathematics, Boston University[EMAIL PROTECTED] 111 Cummington Street, room 261, Boston, MA 02215 (617) 353-5288 184 Nashua Road, Bedford, NH 03110 (603) 471-7128 -- The situation as Mike desribed it: I have a student coming in later to talk about a regression problem. Based on what he's told me so far he is going to be using predicting inter-response intervals to predict inter-stimulus intervals (or vice versa). What bothers me is that he will be collecting data from multiple trials for each subject and then treating the trials as independent replicates. That is, assuming 10 trials/S and 10 S he will act as if he has 100 independent data points for calculating a bivariate regression. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: probability definition
For a quick walk through of various prob. theories, you may consult "The Cambridge Dictionary of Philosophy." pp.649-651. Basically, propensity theory is to deal with the problem that frequentist prob. cannot be applied to a single case. Propensity theory defines prob. as the disposition of a given kind of physical situation to yield an outcome of a given type. The following is extracted from one of my papers. It brielfy talks about the history of classical theory, Reichenbach's frequentism and Fisherian school: Fisherian hypothesis testing is based upon relative frequency in long run. Since a version of the frequentist view of probability was developed by positivists Reichenbach (1938) and von Mises (1964), the two schools of thoughts seem to share a common thread. However, it is not necessarily true. Both Fisherian and positivist's frequency theory were proposed as an opposition to the classical Laplacean theory of probability. In the Laplacean perspective, probability is deductive, theoretical, and subjective. To be specific, this probability is subjectively deduced from theoretical principles and assumptions in the absence of objective verification with empirical data. Assume that every member of a set has equal probability to occur (the principle of indifference), probability is treated as a ratio between the desired event and all possible events. This probability, derived from the fairness assumption, is made before any events occur. Positivists such as Reichenbach and von Mises maintained that a very large number of empirical outcomes should be observed to form a reference class. Probability is the ratio between the frequency of desired outcome and the reference class. Indeed, the empirical probability hardly concurs with the theoretical probability. For example, when a dice is thrown, in theory the probability of the occurrence of number "one" should be 1/6. But even in a million simulations, the actual probability of the occurrence of "one" is not exactly one out of six times. It appears that positivist's frequency theory is more valid than the classical one. However, the usefulness of this actual, finite, relative frequency theory is limited for it is difficult to tell how large the reference class is considered large enough. Fisher (1930) criticized that Laplace's theory is subjective and incompatible with the inductive nature of science. However, unlike the positivists' empirical based theory, Fisher's is a hypothetical infinite relative frequency theory. In the Fisherian school, various theoretical sampling distributions are constructed as references for comparing the observed. Since Fisher did not mention Reichenbach or von Mises, it is reasonable to believe that Fisher developed his frequency theory independently. Backed by a thorough historical research, Hacking (1990) asserted that "to identify frequency theories with the rise of positivism (and thereby badmouth frequencies, since "positivism" has become distasteful) is to forget why frequentism arose when it did, namely when there are a lot of known frequencies." (p.452) In a similar vein, Jones (1999) maintained that "while a positivist may have to be a frequentist, a frequentist does not have to be a positivist." Chong-ho (Alex) Yu, Ph.D., MCSE, CNE Academic Research Professional/Manager Educational Data Communication, Assessment, Research and Evaluation Farmer 418 Arizona State University Tempe AZ 85287-0611 Email: [EMAIL PROTECTED] URL:http://seamonkey.ed.asu.edu/~alex/ = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Regression with repeated measures
Steve Gregorich wrote: Linear mixed models (aka multilelvel models, random coefficient models, etc) as implemented by many software products: SAS PROC MIXED, MIXREG, MLwiN, HLM, etc. You might want to look at some links on my website http://sites.netscape.net/segregorich/index.html There are a few good intros available (some - like Goldstein and Hox's books also on the web): Goldstein, H. (1995). Multilevel statistical models. London: Arnold. Hox, J. J. (1995). Applied multilevel analysis. Amsterdam: TT-Publikaties. Paterson, L., Goldstein, H. (1991). New statistical methods for analyzing social structures: an introduction to multilevel models. British Educational Research Journal, 17, 387-393. Snijders, T. A. B., Bosker, R. J. (1999). Multilevel analysis: an introduction to basic and advanced multilevel modeling. London: Sage. The Snijders Bosker is a very good intro. Kreft de Leeuw also published an intro text (though I haven't read it yet). Thom = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Cronbach's alpha and sample size
Thank you all for the helping answers. I had the problem of obtaining negative Alphas, when some subjects where excluded from analyses (three out of ten). When they were included, I had alphas of .65 to .75 (N items =60). The problem is - as I suspect - that the average interitem correlation is very low and drops below zero when these subjects were excluded. It might interest you, that I'm used to negative correlations in the correlation matrix because I work with difference scores of reation time measures (so there is no directional coding problem). Lots of repeated measures ensure high consistency despite low average inter item correlations and despite some negative correlations between individual measures. Nico -- = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Regression with repeated measures
Donald Burrill wrote: Probably the best approach is the multilevel (aka hierarchical) modelling advocated by previous respondents. Possible problems with that approach: (1) you'll need purpose-built software, which may not be conveniently available at USD; (2) the user is usually required (as I rather vaguely Very good point. recall from a brush with Goldstein's ML3 a decade ago) to specify which (co)variances are to be estimated in the model, both within and between levels, and if your student isn't up to this degree of technical skill, (s)he may not have a clue as to what the output will be trying to say. MlWiN is much easier to use (though does require good knowledge of standard GLM regression equations). The default is just to model the variance at each level, though adding in variance parameters is very easy. I'd love to have a standard GLM program with the same interface (adding, deleting terms from a visual representation of the regression equation). I agree that in lots of cases multilevel modeling may be the "ideal" choice but not sensible in practice (sample size considerations or for some teaching contexts). For some problems, a multilevel model is not required at all. By treating repeated obs as independent N is inflated. It may be sufficient (depending on what effects you want to estimate) just to correct N to reflect this design effect. Snijders and Bosker's book is pretty lucid on this (pp16-24). Thom = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
comparing multiple correlated correlations
OK here's another question from a newbie. In this small sample of 14 subjects, I wanted to compare several correlated correlations: individual's brain volumes correlated with a measure of memory performance. Specifically, I wanted to say that 1 correlation is stronger than the other 3. There's lots out there on just comparing 2 correlations but I wanted to compare all 4 at once. The most appropriate article I found was by Olkin and Finn I. Olkin and J. Finn. Testing correlated correlations. Psychological Bulletin 108(2):330-333, 1990. The problem is that they assume huge sample sizes. I consulted with a statistician and she suggested a jack knife procedure in which I set up the following comparison: r1-average(r2,r3,r4) I iteratively remove each subject and calculate this comparison and the difference of that output from the total group comparison. i.e. r1-average(r2,r3,r4) WITHOUT subject 1 included, r1-average(r2,r3,r4) without subject 2 included... and generate the difference of each of these scores from the total scores. Finally, I generate a confidence interval. If that confidence interval does not include zero, then the comparison is significant. It worked and now I want to cite an appropriate source in the paper. Is there a good reference on similar jack knife procedures? I found this in the spss appendix. M. H. Quenouville. Approximate tests of correlation in time series. Journal of the Royal Statistical Society, Series B 11:68, 1949 Many thanks, Allyson = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
ANN: Book: Causation, Prediction, and Search
I thought readers of sci.stat.edu might be interested in this book. For more information please visit http://mitpress.mit.edu/promotions/books/SPICHF00. Best, Jud Causation, Prediction, and Search second edition Peter Spirtes, Clark Glymour, and Richard Scheines What assumptions and methods allow us to turn observations into causal knowledge, and how can even incomplete causal knowledge be used in planning and prediction to influence and control our environment? In this book Peter Spirtes, Clark Glymour, and Richard Scheines address these questions using the formalism of Bayes networks, with results that have been applied in diverse areas of research in the social, behavioral, and physical sciences. The authors show that although experimental and observational study designs may not always permit the same inferences, they are subject to uniform principles. They axiomatize the connection between causal structure and probabilistic independence, explore several varieties of causal indistinguishability, formulate a theory of manipulation, and develop asymptotically reliable procedures for searching over equivalence classes of causal models, including models of categorical data and structural equation models with and without latent variables. The authors show that the relationship between causality and probability can also help to clarify such diverse topics in statistics as the comparative power of experimentation versus observation, Simpson's paradox, errors in regression models, retrospective versus prospective sampling, and variable selection. The second edition contains a new introduction and an extensive survey of advances and applications that have appeared since the first edition was published in 1993. Peter Spirtes is Professor of Philosophy at the Center for Automated Learning and Discovery, Carnegie Mellon University. Clark Glymour is Alumni University Professor of Philosophy at Carnegie Mellon University and Valtz Family Professor of Philosophy at the University of California, San Diego. He is also Distinguished External Member of the Center for Human and Machine Cognition at the University of West Florida, and Adjunct Professor of Philosophy of History and Philosophy of Science at the University of Pittsburgh. Richard Scheines is Associate Professor of Philosophy at the Center for Automated Learning and Discovery, and at the Human Computer Interaction Institute, Carnegie Mellon University. 7 x 9, 496 pp., 225 illus., cloth ISBN 0-262-19440-6 Adaptive Computation and Machine Learning series A Bradford Book = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
