{smcl} {cmd:help mata _somdtransf} {hline} {title:Title} {p 4 4 2} {bf:_somdtransf() -- Transformations used by somersd} {title:Syntax} {p 8 8 2} {it:void}{bind: } {cmd:_somdtransf(}{it:transf}{cmd:,} {it:theta}{cmd:,} {it:zeta} [ {cmd:,} {it:dzeta} ]{cmd:)} {p 4 4 2} where {it:transf}: {it:string scalar} {it:theta}: {it:real matrix} {it:zeta}: {it:real matrix} {it:dzeta}: {it:real matrix} {title:Description} {p 4 4 2} This function is used by {helpb somersd} to perform the transformations specified by the {cmd:transf()} option and described in the file {hi:somersd.pdf}, which is distributed with the {cmd:somersd} package. {p 4 4 2} {cmd:_somdtransf(}{it:transf}{cmd:,} {it:theta}{cmd:,} {it:zeta}{cmd:,} {it:dzeta}{cmd:)} inputs a string scalar in {it:transf}, which specifies one of the transformations used by the {cmd:transf()} option of {cmd:somersd}, and a matrix {it:theta}, containing values for Somers' {it:D} or Kendall's tau-a. It outputs a matrix {it:zeta}, with the same dimensions as {it:theta}, containing the transformed values, and, optionally, a matrix {it:dzeta}, with the same dimensions, containing the derivatives of the transformed values with respect to the untransformed values. Either {it:zeta} or {it:dzeta}, but not both, may be the same matrix as {it:theta}, which is then overwritten. Some transformations, or their derivatives, are undefined for untransformed values of 1 and -1 and may be too large to be calculated at values close to 1 or -1. In these cases, {cmd:somdtransf()} uses a maximum value {it:thetamax}, slightly less than one, and sets the transformed values and their derivatives to the transformed value and derivative for {it:thetamax} for untransformed values above {it:thetamax} and sets the transformed values and their derivatives to the transformed value and derivative for {it:-thetamax} for untransformed values below {it:-thetamax}. The value of {it:thetamax} depends on the transformation specified by the string scalar {it:transf}. If the string scalar {it:transf} contains a value other than one of the transformation names recognized by the {cmd:transf()} option of {helpb somersd}, then all the transformed values and their derivatives are set to missing. {title:Remarks} {p 4 4 2} The value of the maximum untransformed value {it:thetamax} depends on the value of {it:transf}, which specifies a transformation recognized by the {cmd:transf()} option of {helpb somersd}. The recognized values, and corresponding maximum untransformed values, are as follows: {title:{it:transf}} {title:{it:thetamax}} {hi:iden} 1 {hi:z} 0.999999999999999 {hi:asin} 0.999999999999999 {hi:rho} 1 {hi:zrho} 0.99999999 {hi:c} 1 {p 4 4 2} These values ensure that any value of Somers' {it:D} or Kendall's tau-a from -1 to 1 will have a nonmissing transformed value and derivative. These values will not be strictly correct for untransformed values of magnitude greater than {it:thetamax}. However, confidence intervals generated by {helpb somersd} for such untransformed values should probably not be taken seriously, because these confidence intervals are calculated by the delta-jackknife method and work by the Central Limit Theorem, which does not work well for such extreme population values of Somers' {it:D} and Kendall's tau-a. The formulas for all these transformations, and for their derivatives and inverses, are given in the manual {hi:somersd.pdf}, distributed with the {helpb somersd} package. {title:Conformability} {cmd:_somdtransf(}{it:transf}{cmd:,} {it:theta}{cmd:,} {it:zeta}{cmd:,} {it:dzeta}{cmd:)}: {it:transf}: 1 {it:x} 1 {it:theta}: {it:M x N} {it:zeta}: {it:M x N} {it:dzeta}: {it:M x N} {title:Diagnostics} {p 4 4 2} {cmd:_somdtransf(}{it:transf}{cmd:,} {it:theta}{cmd:,} {it:zeta}{cmd:,} {it:dzeta}{cmd:)} returns missing values of {it:zeta} and {it:dzeta} for values of {it:theta} greater than 1, or less than -1, or for unrecognized values of {it:transf}. {title:Source code} {p 4 4 2} {view _somdtransf.mata, adopath asis:_somdtransf.mata} {title:Author} {p 4 4 2} Roger Newson, Imperial College London, UK.{break} Email: {browse "mailto:r.newson@imperial.ac.uk":r.newson@imperial.ac.uk} {title:Also see} {p 4 13 2} Manual: {hi:[M-0] intro} {p 4 13 2} Online: {helpb mata}, {break} {helpb somersd} (if installed) {p_end}