[Date Prev][Date Next][Thread Prev][Thread Next][Date index][Thread index]

From |
Michael Ingre <[email protected]> |

To |
<[email protected]> |

Subject |
st: Rankit, pearson and polychoric correlations [was: Ordinal tointerval assuming normality] |

Date |
Mon, 20 Oct 2003 17:47:17 +0200 |

Thank you Nick Cox, your neat suggestion -almost- (I think) did the trick. > . sysuse auto > . ssc inst egenmore > . egen ridit = ridit(rep78) > . gen pseudogauss = invnorm(ridit) > . tabdisp rep78, c(ridit pseudogauss) But, wouldn't the estimation using ridit scores (mean rank / sample size) bias z slightly towards zero when you have many observations/category? That is, z-scores would increase more to the left than decrease to the right of the rank mean within a category (on the left hand size of the distribution). > Is this not (related to) the > rankit transformation of Fisher and Yates? Yes, I think you are right. And I tried to find out more about it however, this procedure is not mentioned in any textbook that I could find. Searching the net gave me a few hits. It is close to your suggestion: rankit = invnorm( (mean rank-0.375)/sample size+0.25) ) Polychoric correlations (PC) is related to this issue as well and this was pointed out by Bill Magee (off-list). Learning about PC was what prompted me towards this question in the first place. PCs could be estimated with LISREL (PRELIS) and SAS. In PC, the calculation is based on thresholds between categories assuming a -bivariate- normal distribution. If I understand PC correct however, the thresholds are recalculated for every bivariate PC. They are likely vary slightly between PCs and would be problematic in multivariate procedures (even in LISREL) and when comparing estimates between multiple bivariate analyses. The calculation of thresholds should however, yield unbiased z-scores: threshold = invnorm(max unique rank/category [or cumulative freq]/sample size) The above formula correctly reproduces the -univariate- thresholds calculated by PRELIS. However, it is not usable as is, because there is no valid threshold for the highest category - invnorm(1). My questions -------------- I'm seeking an alternative to PCs that would enable me to use standard statistical procedures (pearson, anova, regress etc.) and get correct estimates of the latent variable assuming a normal distribution. Nick pointed out that the assumption of normality is often violated. This is true in my case also. However, in a large population sample (like all twins in Sweden) with low drop out this would seem to me as an appropriate approximation. Although, one would expect a slightly higher drop out in some categories (for example poor subjective health). 1) The invnorm(ridit) and the similar rankit procedure seems to be a possible solution. But -rankit- is not very well known or used. Why, am I missing something important? 2) Just to confirm, am I right in assuming a slight bias in z in the rankit procedure? 3) The slight bias in z could be acceptable but is there a way of correcting for this bias? 4) What does the constants do in the rankit procedures? 5) PCs could be used in LISREL however, the manual states that this violates the assumption behind ML and estimation has to be done with WLS. (I think this might be due to the inconsistencies in the covariance matrix). But, what about using rankit (or similar) transformations, treat them as continuous and use ML? Thank you all for you patience. And feel free to comment or answer one or more questions. Michael Ingre ----------------- PhD-student Institution for Psychology Stockholm University National Institute for Psychoscial Medicine * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:

**References**:**st: RE: Ordinal to interval assuming normality***From:*"Nick Cox" <[email protected]>

- Prev by Date:
**st:generalized residual** - Next by Date:
**RE: st: RE: Re: Cluster Analysis** - Previous by thread:
**st: RE: Ordinal to interval assuming normality** - Next by thread:
**st: RE: Rankit, pearson and polychoric correlations [was: Ordinal tointerval assuming normality]** - Index(es):

© Copyright 1996–2024 StataCorp LLC | Terms of use | Privacy | Contact us | What's new | Site index |