Bioequivalence and Bioavailability Forum • Studentized Residuals

Risherd
☆

Mexico,
2012-01-07 01:46
(4873 d 13:14 ago)

Posting: # 7877
Views: 8,525

Studentized Residuals [Outliers]

Hello!

One of the test for outlier detection is the use of studentized residuals, but I have a doubt of what is the correct formula to use, I know the following formula Stud-Res= Residual/sqrroot(MSerror), however today I read that this Studentized Residuals are obtained with this formula Stu-Res=residual/(sqrroot(1-hii), so this is when I ask for your help, are this two formulas the same? or which one is the correct to use?.

Last question, what is the value in which I can consider a value as outlier ±2 or ±4?

Thank you for your answer and excuse my lack of knowledge in this issue.

Risherd.

Helmut
★★★

Vienna, Austria,
2012-01-09 19:02
(4870 d 19:58 ago)

@ Risherd
Posting: # 7885
Views: 7,433

Studentized Residuals

Post reply

Dear Ricardo!

❝ One of the test for outlier detection is the use of studentized residuals, but I have a doubt of what is the correct formula to use, I know the following formula Stud-Res= Residual/sqrroot(MSerror), however today I read that this Studentized Residuals are obtained with this formula Stu-Res=residual/(sqrroot(1-hii), […] are this two formulas the same? or which one is the correct to use?

I’m familiar with the first one. Where do you get h_ii from? Or in other words what are the indices ‘i’ denoting? I only know a similar terminology used by Willavize & Morgenthin¹ and Schall et al.²: h_ijk, where i is the subject’s index (i=1…n), j and k the indices of sequences and repetitions of treatments in a replicate design (e.g., full replicate j=1…2, k=1…2).

❝ Last question, what is the value in which I can consider a value as outlier ±2 or ±4?

Schall et al.² recommend Grubbs’ critical values (α 0.05, two-sided), f.i.:

n crit. 12 ±2.41156 16 ±2.58568 24 ±2.80155 32 ±2.93805 40 ±3.03610 48 ±3.11180 56 ±3.17302 64 ±3.22418

If your statistical software doesn’t provide Grubbs’ critical values, you will get them from the R package outliers. Code:

library(outliers) lo <- 12 # lower sample size for Grubb’s test (min: 3) hi <- 64 # upper limit of sample size n <- seq(lo, hi) # sample sizes grubbs.crit <- data.frame(n=n, lo=NA, hi=NA) for (j in seq_along(n)) { grubbs.crit[j, "hi"] <- qgrubbs(0.975, n=n[j], type=10) } grubbs.crit$lo <- -grubbs.crit$hi print(grubbs.crit, row.names=FALSE)

❝ […] excuse my lack of knowledge in this issue.

No worries – you are not alone. I’m struggling myself.

Willavize SA, Morgenthin EA. Comparision of models for average bioequivalence in replicate crossover designs. Pharmaceut Stat. 2006;5(3):201–11. doi:10.1002/pst.212.
Schall R, Endrényi L, Ring A. Residuals and Outliers in Replicate Design Crossover Studies. J Biopharmaceut Stat. 2010;20:835–49. doi:10.1080/10543401003618876

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Risherd
☆

Mexico,
2012-01-09 23:48
(4870 d 15:12 ago)

@ Helmut
Posting: # 7887
Views: 7,326

Studentized Residuals

Post reply

Hello HS!

Thank you for your answer, and answering your question:

❝ Where do you get h_ii from? Or in other words what are the indices ‘i’ denoting?.

This h_ii terminology is the ith diagonal element of H that is used in the calculation of the internally Studentized residuals⁽¹⁾.

In the Mexican regulation the criterion to decret a value as outlier is to obtain a studentized residual of ±4. In the paper of Gray & William, 1994 I read that "it is impossible to obtain a value of ei/s larger than 4.0" also Drapper and Smith 1981⁽²⁾, stated that approximately 95% of the ei/s values should lie between -2 and 2 but pointed out that the ei/s values are not independent and do not have unit variance.

Theres is draft of the next mexican NOM (Mexican Official Norm) of 2009 (!!) which will consider a value as outlier with more than ±2 studentized residuals.

Maybe I didn't explain myself in my first post so this is my doubt and this killing me inside :-D

❝ ❝ which..value..±2 or ±4?

Adding to this calculus of the internally studentized residual I use the Grubbs test as well (at critical value α=0.05). I do the procedure on a worksheet in Excel but thank you for the advice, I will start using R’s package http://cran.r-project.org/web/packages/outliers/index.html, it'll come handy!

One more question, Which critical alfa value would be appropriate for an outlier test 0.05 or 0.02?

Best regards,
Ricardo.

(1) JB Gray and WH Woodwall
The maxium size of Standardized and Internally Studentized Residuals in Regression Analysis
American Statistician 48(2), 111-113 (1994)

(2) NR Draper and H Smith
Applied Regression Analysis
Applied Regression Analysis (2nd Ed.), New York:John Wiley (1981).