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Correlations of variables with BRR-based significance calculations

brrcorr[varlist] [weight] [ifexp] [inrange] [,pwobssigprint(#)star(#)bonferronisidak

brrweight(varlist)fay(#)dof(#)]

by...:may be used with the above commands; see by.

pweightsare allowed; see weights.

Description

brrcorrdisplays the correlation matrix forvarlistor, ifvarlistis not specified, for all variables in the data. Observations are excluded from the calculation due to missing values on a casewise basis, unless thepwoption is specified.Significance levels of the correlations are based on standard errors that are calculated using a series of user-supplied replication weights, by the balanced repeated replication (BRR) method. This is an alternate method to the Taylor series linearization methods used by Stata's svy-based commands.

Options

brrweight()specifies the list of variables that contain the replicate weights for the dataset. The standard errors for the model are based on the variation in the estimates generated across the various weights.A set of

brrweightsis required for the analysis. Once the brrweights are specified they are stored as a characteristic of the dataset and need not be respecified in subsequent command.

fay()specifies the k value that should be used for weighting the estimates, based on Fay's method. The default is zero, meaning that simple averaging will be used. As with the replicate weights, the value for fay() is stored as a characteristic of the dataset once it is specified, and need not be re-specified in subsequent commands.

dof()specifies the degrees of freedom for model fit and t-statistics. The default is to use the number of replications.

pwspecifies that observations are to be excluded from the calculations on a pairwise basis. The default is casewise.

obsadds a line to each row of the matrix reporting the number of observations used in calculating the correlation coefficient.

sigadds a line to each row of the matrix reporting the significance level of each correlation coefficient.

print(#)specifies the significance level of correlation coefficients to be printed. Coefficients with larger significance levels are left blank.print(10)orprint(.1)would list only coefficients significant at the 10% level or better.

star(#)specifies the significance level of coefficients to be starred.star(5)orstar(.05)would star all coefficients significant at the 5% level or better.

bonferronimakes the Bonferroni adjustment to calculated significance levels. This affects printed significance levels and theprint()andstar()options."pwcorr, print(.05) bonferroni"prints coefficients with Bonferroni-adjusted significance levels of .05 or less.

sidakmakes the Sidak adjustment to calculated significance levels. This affects printed significance levels and theprint()andstar()options."pwcorr, print(.05) sidak"prints coefficients with Sidak-adjusted significance levels of .05 or less.

Examples. brrcorr dvcrate medage [pw=wgt], brrw(bw*)

. brrcorr mrgrate dvcrate medage, pw obs sig

Methods and formulaePoint estimates are calculated using aweights. Significance levels of the estimated correlations are based on the variance matrix of each estimate, calculated as follows:

G V = c * SUM [ (r - r(i))^2 ] i=1

where r is the estimated coefficient based on the full sample weights, r(i) is the estimated coefficient using the i'th set of replicate weights, G is the number of replicates, and c is a constant defined as:

1 / G for standard BRR (i.e. fay==0), or

1 / (G*(1-k)^2) for Fay's method. For calculation of variances and significances, the correlations are first transformed using Fisher's Z transformation, in order to normalize the distribution.

Saved Results

brrcorrsaves in r() the following for the last-calculated correlation:rho the estimated correlation coefficient N the number of observations p the p-level

AcknowledgementsThese commands consists largely of the ado file code from official Stata's

pwcorrcommand. I would like to thank Bobby Gutierrez at StataCorp for advice on implementation of BRR.

AuthorNick Winter Cornell University nw53@cornell.edu