multreg.second: A multiple regression analysis using published work
In rpsychi: Statistics for psychiatric research

Description Usage Arguments Details Value Author(s) References See Also Examples

multreg.second conducts a multiple regression analysis using published work.

1 2	multreg.second(formula, corr, n, m = NULL, sd = NULL, sig.level = 0.05, digits = 3)

`formula`	two-sided formula; the left-hand-side of which gives one dependent variable containing a numeric variable, and the right-hand-side of several independent variables containing a numeric variable
`corr`	a matrix or data frame contains the correlation matrix
`n`	a numeric contains the sample size
`m`	a numeric vector contains the means (default NULL)
`sd`	a numeric vector contains the sample/unbiased standard deviations (default NULL)
`sig.level`	a numeric contains the significance level (default 0.05)
`digits`	the specified number of decimal places (default 3)

This function conducts a multiple regression analysis using published work. The dependent variable and independent variables should be a numeric vector. In this function, you cannot specify any interaction nor any curvilinear effect. If you do not specify m and sd, raw.estimates will not be obtained. Statistical power is calculated using the following specifications:

(a) small (R^{2} = 0.02), medium (R^{2} = 0.13), and large (R^{2} = 0.26) population effect sizes, according to the interpretive guideline for effect sizes by Cohen (1992)

(b) sample size specified by data

(d) numbers of independent variable specified by formula

`corr.partial.corr`	returns a product-moment correlation matrix (lower triangle) and a partial correlation matrix given all remaining variables (upper triangle)
`corr.confidence`	returns lower and upper confidence limits (lower and upper triangles, respectively)
`omnibus.es`	returns a coefficient of determination and its' confidence interval
`raw.estimates`	returns partial regression coefficients, their confidence intervals, and standard errors
`standardized.estimates`	returns standardized partial regression coefficients, their confidence intervals, and standard errors
`power`	returns statistical power for detecting small (R^{2} = 0.02), medium (R^{2} = 0.13), and large (R^{2} = 0.26) population effect sizes

Yasuyuki Okumura
Department of Social Psychiatry,
National Institute of Mental Health,
National Center of Neurology and Psychiatry
yokumura@blue.zero.jp

Cohen J (1992) A power primer. Psychological Bulletin, 112, 155-159.

Cohen J, Cohen P, Aiken LS (2003) Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed). Mahwah, NJ: Erlbaum.

Smithson M (2001) Correct confidence intervals for various regression effect sizes and parameters: The importance of noncentral distributions in computing intervals, 61, 605-632.

multreg, samplesize.rsq

##Cohen (2003) Table 3.5.1
dat <- data.frame(
salary = c(51876, 54511, 53425, 61863, 52926, 47034, 66432, 61100, 41934, 
  47454, 49832, 47047, 39115, 59677, 61458, 54528, 60327, 56600, 
  52542, 50455, 51647, 62895, 53740, 75822, 56596, 55682, 62091, 
  42162, 52646, 74199, 50729, 70011, 37939, 39652, 68987, 55579, 
  54671, 57704, 44045, 51122, 47082, 60009, 58632, 38340, 71219, 
  53712, 54782, 83503, 47212, 52840, 53650, 50931, 66784, 49751, 
  74343, 57710, 52676, 41195, 45662, 47606, 44301, 58582),
pubs  = c(18, 3, 2, 17, 11, 6, 38, 48, 9, 22, 30, 21, 
  10, 27, 37, 8, 13, 6, 12, 29, 29, 7, 6, 69, 11, 9, 
  20, 41, 3, 27, 14, 23, 1, 7, 19, 11, 31, 9, 12, 32, 
  26, 12, 9, 6, 39, 16, 12, 50, 18, 16, 5, 20, 50, 
  6, 19, 11, 13, 3, 8, 11, 25, 4),
cits = c(50, 26, 50, 34, 41, 37, 48, 56, 19, 29, 
    28, 31, 25, 40, 61, 32, 36, 69, 47, 29, 35, 
    35, 18, 90, 60, 30, 27, 35, 14, 56, 50, 25, 
    35, 1, 69, 69, 27, 50, 32, 33, 45, 54, 47, 29, 
    69, 47, 43, 55, 33, 28, 42, 24, 31, 27, 
    83, 49, 14, 36, 34, 70, 27, 28)   )

multreg.second(salary~ pubs + cits, corr=cor(dat), n= nrow(dat))
multreg.second(salary~ pubs + cits, corr=cor(dat), n= nrow(dat), 
        m = apply(dat, 2, mean), sd=apply(dat, 2, sd))