This is in response to a query (copied below) from Hakan Demirtas. Since I did not keep the original, I am taking it from the archives. Therefore this may initiate a new thread ... :-(
There has been one response so far, which gave no help. On Fri, Apr 2, 2010 at 7:25 PM, HAKAN DEMIRTAS <demir...@uic.edu> wrote: > Hi, > Is there any R library/package that calculates tetrachoric > correlations from given marginals and Pearson correlations > among ordinal variables? > > Inputs to polychor function in polycor package are either > contingency tables or ordinal data themselves. I am looking > for something that takes marginal distributions and Pearson > correlation as inputs. > > For example, Y1=(1,2,3) with P(Y1=1)=0.3, P(Y1=2)=0.5, P(Y1=3)=0.2 > and Y2=(1,2) with P(Y2=1)=0.6, P(Y2=2)=0.4, and corr(Y1,Y2)=0.5 > (Pearson correlation among ordinal variables) > > How do I calculate the tetrachoric correlation here? > > Thanks, > Hakan Demirtas First, there is some imprecision in the query! Tetrachoric correlation refers to 2x2 tables, whereas your example is 3x2, so polychoric correlation would be appropriate. Searching the R site on pearson tetrachoric returns one useful hit, the function phitopoly in the 'psych' package: http://finzi.psych.upenn.edu/R/library/psych/html/phi2poly.html phi2poly {psych} R Documentation Convert a phi coefficient to a polychoric correlation Description Given a phi coefficient (a Pearson r calculated on two dichotomous variables), and the marginal frequencies (in percentages), what is the corresponding estimate of the polychoric correlation? Given a two x two table of counts a b c d The phi coefficient is (a - (a+b)*(a+c))/sqrt((a+b)(a+c)(b+d)(c+c)). This function reproduces the cell entries for specified marginals and then calls John Fox's polychor function. Usage phi2poly(ph, cp, cc) Arguments ph phi cp probability of the predictor -- the so called selection ratio cc probability of the criterion -- the so called success rate. Note that this function specifies "two dichotomous variables", otherwise speaking a 2x2 situation. Hence, given the marginal probabilities and the Pearson correlation for a 2x2 table, this function will calculate the tetrachoric (= 2x2 polychoric) correlation. This is possible because, given the marginals, there is only one degree of freedom remaining, and the value of the Pearson coefficient then serves to determine the table of probabilities in full. Second, note that this well not be the case for a general rxc table and, in particular, for your 3x2 example. Given the marginal probabilities, there will be 2 degrees of freedom remaining, and the additional information that the Pearson correlation between Y1 and Y2 has a particular value still leaves one degree of freeom. So your question does not have a determinate answer in the 2x3 (or higher) case. You would need to use additional information. Indeed, an R site search on pearson polychoric seems to give no relevant results. Hoping this helps, Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <ted.hard...@manchester.ac.uk> Fax-to-email: +44 (0)870 094 0861 Date: 04-Apr-10 Time: 16:25:58 ------------------------------ XFMail ------------------------------ ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
