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457 lines
14 KiB
Plaintext
457 lines
14 KiB
Plaintext
9 months ago
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*! version 1.1.0 PR 30aug2005.
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*
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* Recent history of uvis
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* 1.1.0 03aug2005 Replace -draw- option with -match-. Default becomes draw.
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* With prediction matching, randomly sort observations with identical predictions.
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* Order variables in chained equations in order of increasing missingness.
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* 1.0.4 21jun2005 Add sort, stable to enable reproducibility imputations with given seed
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*
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program define uvis, rclass sortpreserve
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version 8
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gettoken cmd 0 : 0
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if substr("`cmd'",1,3)=="reg" {
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local cmd regress
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}
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local normal=("`cmd'"=="regress")|("`cmd'"=="rreg")
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local binary=("`cmd'"=="logit")|("`cmd'"=="logistic")
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local catcmd=("`cmd'"=="mlogit")|("`cmd'"=="ologit")
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if !`normal' & !`binary' & !`catcmd' {
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di in red "invalid or unrecognised command, `cmd'"
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exit 198
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}
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syntax varlist(min=2 numeric) [if] [in] [aweight fweight pweight iweight] , Gen(string) /*
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*/ [ noCONStant Delta(real 0) BOot MAtch REPLACE SEed(int 0) * ]
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if "`replace'"=="" {
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confirm new var `gen'
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}
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if "`match'"=="match" {
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di as text "[imputing by prediction matching" _cont
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}
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else di as text "[imputing by drawing from conditional distribution" _cont
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if "`boot'"=="" {
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di as text " without bootstrap]"
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}
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else di as text " with bootstrap]"
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if "`constant'"=="noconstant" {
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local options "`options' nocons"
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}
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gettoken y xvars : varlist
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tempvar touse
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quietly {
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marksample touse, novarlist
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markout `touse' `xvars' /* note: does not include `y' */
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if `seed'!=0 {
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set seed `seed'
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}
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* Deal with weights
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frac_wgt `"`exp'"' `touse' `"`weight'"'
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local wgt `r(wgt)'
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* Code types of missings: 1=non-missing y, 2=missing y, 3=other missing
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tempvar obstype yimp
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gen byte `obstype'=1*(`touse'==1 & !missing(`y')) /*
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*/ +2*(`touse'==1 & missing(`y')) /*
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*/ +3*(`touse'==0)
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count if `obstype'==1
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local nobs=r(N)
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count if `obstype'==2
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local nmis=r(N)
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local type: type `y'
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gen `type' `yimp'=.
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* Fit imputation model
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`cmd' `y' `xvars' `wgt', `options'
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tempname b e V chol bstar
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tempvar xb u
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matrix `b'=e(b)
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matrix `e'=e(b)
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matrix `V'=e(V)
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local colsofb=colsof(`b')
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* Check for zeroes on the diagonal of V and replace them with 1.
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* Otherwise this makes the matrix non-positive definite.
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* Occurs when e.g. logit drops variables, giving zero variances.
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* !! Is this safe to do?
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if diag0cnt(`V')>0 {
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forvalues j=1/`colsofb' {
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if `V'[`j',`j']==0 {
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matrix `V'[`j',`j']=1
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}
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}
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}
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matrix `chol'=cholesky(`V')
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if `catcmd' {
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tempname cat
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local nclass=e(k_cat) /* number of classes in (ordered) categoric variable */
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matrix `cat'=e(cat) /* row vector giving actual category values */
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local cuts=`nclass'-1
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}
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* Draw beta, and if necessary rmse, for proper imputation
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if `normal' {
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* draw rmse
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local rmse=e(rmse)
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local df=e(df_r)
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local chi2=2*invgammap(`df'/2,uniform())
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local rmsestar=`rmse'*sqrt(`df'/`chi2')
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matrix `chol'=`chol'*sqrt(`df'/`chi2')
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}
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* draw beta
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forvalues i=1/`colsofb' {
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matrix `e'[1,`i']=invnorm(uniform())
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}
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matrix `bstar'=`b'+`e'*`chol''
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if "`boot'"=="" {
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* Based on Ian White's code to implement van Buuren et al (1999).
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* draw y
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gen `u'=uniform()
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if `normal' | `binary' {
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* in normal or binary case, impute by sampling conditional distribution
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* or by prediction matching
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if "`match'"=="match" {
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* prediction matching
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tempvar etaobs etamis
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matrix score `etaobs'=`b' if `obstype'==1
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matrix score `etamis'=`bstar' if `obstype'==2
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* Include non-response location shift, delta.
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if `delta'!=0 {
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replace `etamis'=`etamis'+`delta'
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}
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match_normal `obstype' `nobs' `nmis' `etaobs' `etamis' `yimp' `y'
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}
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else {
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* sampling conditional distribution
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matrix score `xb'=`bstar' if `touse'
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if `normal' {
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replace `yimp'=`xb'+`rmsestar'*invnorm(`u')
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}
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else replace `yimp'=`u'<1/(1+exp(-`xb')) if !missing(`xb')
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}
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}
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else { /* catcmd */
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if "`match'"=="match" { // prediction matching
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* predict class-specific probabilities and convert to logits
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if "`cmd'"=="ologit" {
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* Predict index independent of cutpoints
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* (note use of forcezero option to circumvent missing _cut* vars)
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matrix score `xb'=`b' if `touse', forcezero
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* predict cumulative probabilities for obs data and hence logits of class probs
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forvalues k=1/`nclass' {
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tempvar etaobs`k' etamis`k'
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if `k'==`nclass' {
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gen `etaobs`nclass''=log((1-`p`cuts'')/`p`cuts'') if `obstype'==1
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}
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else {
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tempvar p`k'
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local cutpt=`b'[1, `k'+`colsofb'-`cuts']
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* 1/(1+exp(-... is probability of being in category 1 or 2 or ... k
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gen `p`k''=1/(1+exp(-(`cutpt'-`xb')))
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if `k'==1 {
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gen `etaobs`k''=log(`p`k''/(1-`p`k'')) if `obstype'==1
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}
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else {
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local k1=`k'-1
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gen `etaobs`k''=log((`p`k''-`p`k1'')/(1-(`p`k''-`p`k1''))) /*
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*/ if `obstype'==1
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}
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}
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}
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drop `xb'
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matrix score `xb'=`bstar' if `touse', forcezero
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* predict cumulative probabilities for missing data and hence logits of class probs
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forvalues k=1/`nclass' {
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if `k'==`nclass' {
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gen `etamis`nclass''=log((1-`p`cuts'')/`p`cuts'') if `obstype'==2
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}
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else {
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local cutpt=`bstar'[1, `k'+`colsofb'-`cuts']
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replace `p`k''=1/(1+exp(-(`cutpt'-`xb')))
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if `k'==1 {
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gen `etamis`k''=log(`p`k''/(1-`p`k'')) if `obstype'==2
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}
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else {
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local k1=`k'-1
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gen `etamis`k''=log((`p`k''-`p`k1'')/(1-(`p`k''-`p`k1''))) /*
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*/ if `obstype'==2
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}
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}
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}
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}
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else { /* mlogit */
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* predict cumulative probabilities for obs data and hence logits of class probs
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* care needed dealing with different possible base categories
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tempvar sumexp
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local basecat=e(basecat) /* actual basecategory chosen by Stata */
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gen `sumexp'=0 if `touse'
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forvalues k=1/`nclass' {
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tempvar etaobs`k' etamis`k' xb`k'
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local thiscat=`cat'[1,`k']
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if `thiscat'==`basecat' {
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gen `xb`k''=0 if `touse'
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}
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else matrix score `xb`k''=`b' if `touse', equation(`thiscat')
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replace `sumexp'=`sumexp' + exp(`xb`k'')
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}
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forvalues k=1/`nclass' {
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* formula for logit of class prob derived from Pk in Stata mlogit entry
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gen `etaobs`k''=`xb`k''-log(`sumexp'-exp(`xb`k'')) if `obstype'==1
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}
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* same for missing obs
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replace `sumexp'=0
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forvalues k=1/`nclass' {
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cap drop `xb`k''
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local thiscat=`cat'[1,`k']
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if `thiscat'==`basecat' {
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gen `xb`k''=0 if `touse'
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}
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else matrix score `xb`k''=`bstar' if `touse', equation(`thiscat')
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replace `sumexp'=`sumexp' + exp(`xb`k'')
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}
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forvalues k=1/`nclass' {
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* formula for logit of class prob derived from Pk in Stata mlogit entry
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gen `etamis`k''=`xb`k''-log(`sumexp'-exp(`xb`k'')) if `obstype'==2
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}
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}
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* match
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sort `obstype', stable
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tempvar order distance
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gen `distance'=.
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gen long `order'=_n
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* For each missing obs j, find index of obs whose etaobs is closest to prediction [j].
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forvalues i=1/`nmis' {
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local j=`i'+`nobs'
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* calc summed absolute distances between etamis* and etaobs*
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replace `distance'=0 in 1/`nobs'
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forvalues k=1/`nclass' {
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replace `distance'=`distance'+abs(`etamis`k''[`j']-`etaobs`k'') in 1/`nobs'
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}
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* Find index of smallest distance between etamis* and etaobs*
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sort `distance'
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local index=`order'[1]
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* restore correct order
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sort `order'
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replace `yimp'=`y'[`index'] in `j'
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}
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}
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else { // draw
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* sampling conditional distribution
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replace `yimp'=`cat'[1,1]
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if "`cmd'"=="ologit" {
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* Predict index independent of cutpoints
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* (note use of forcezero option to circumvent missing _cut* vars)
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matrix score `xb'=`bstar' if `touse', forcezero
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forvalues k=1/`cuts' {
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* 1/(1+exp(-... is probability of being in category 1 or 2 or ... k
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local cutpt=`bstar'[1, `k'+`colsofb'-`cuts']
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replace `yimp'=`cat'[1,`k'+1] if `u'>1/(1+exp(-(`cutpt'-`xb')))
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}
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}
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else { /* mlogit */
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* care needed dealing with different possible base categories
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tempvar cusump sumexp
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local basecat=e(basecat) /* actual basecategory chosen by Stata */
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gen `sumexp'=0 if `touse'
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forvalues i=1/`nclass' {
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tempvar xb`i'
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local thiscat=`cat'[1,`i']
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if `thiscat'==`basecat' {
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gen `xb`i''=0 if `touse'
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}
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else matrix score `xb`i''=`bstar' if `touse', equation(`thiscat')
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replace `sumexp'=`sumexp' + exp(`xb`i'')
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}
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gen `cusump'=exp(`xb1')/`sumexp'
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forvalues i=2/`nclass' {
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replace `yimp'=`cat'[1,`i'] if `u'>`cusump'
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replace `cusump'=`cusump'+exp(`xb`i'')/`sumexp'
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replace `yimp'=. if missing(`xb`i'')
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}
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}
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}
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}
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}
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else {
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* Bootstrap method
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if "`match'"=="match" { /* match */
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if `catcmd' {
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* predict class-specific probabilities and convert to logits
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forvalues k=1/`nclass' {
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local outk=`cat'[1,`k']
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tempvar etaobs`k' etamis`k'
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predict `etaobs`k'' if `obstype'==1, outcome(`outk') /* probability */
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replace `etaobs`k''=log(`etaobs`k''/(1-`etaobs`k'')) /* logit */
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}
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}
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else { /* normal and binary cases */
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tempvar etaobs etamis
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predict `etaobs' if `obstype'==1, xb
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}
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}
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* Bootstrap observed data
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tempvar wt
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gen double `wt'=.
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bsample if `obstype'==1, weight(`wt')
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if "`wgt'"!="" {
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replace `wt' `exp'*`wt'
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local w [`weight'=`wt']
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}
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else local w [fweight=`wt']
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`cmd' `y' `xvars' `w', `options'
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if `catcmd' {
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if e(k_cat)<`nclass' {
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di as error "cannot predict outcome for all classes in bootstrap sample;"
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di as error "probably one or more classes has a low frequency in the original data:"
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di as error "try amalgamating small classes of `y' and rerunning"
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exit 303
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}
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}
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if "`match'"=="match" {
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if `catcmd' {
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* predict class-specific probabilities and convert to logits
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forvalues k=1/`nclass' {
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local outk=`cat'[1,`k']
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predict `etamis`k'' if `obstype'==2, outcome(`outk') /* probability */
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replace `etamis`k''=log(`etamis`k''/(1-`etamis`k'')) /* logit */
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}
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* match
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sort `obstype', stable
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tempvar order distance
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gen `distance'=.
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gen long `order'=_n
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* For each missing obs j, find index of obs whose etaobs is closest to prediction [j].
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forvalues i=1/`nmis' {
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local j=`i'+`nobs'
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* calc summed absolute distances between etamis* and etaobs*
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replace `distance'=0 in 1/`nobs'
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forvalues k=1/`nclass' {
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replace `distance'=`distance'+abs(`etamis`k''[`j']-`etaobs`k'') in 1/`nobs'
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}
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* Find index of smallest distance between etamis* and etaobs*
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sort `distance'
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local index=`order'[1]
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* restore correct order
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|
sort `order'
|
||
|
|
replace `yimp'=`y'[`index'] in `j'
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else { /* normal and binary */
|
||
|
|
predict `etamis' if `obstype'==2, xb
|
||
|
|
|
||
|
|
* Include non-response location shift, delta.
|
||
|
|
if `delta'!=0 {
|
||
|
|
replace `etamis'=`etamis'+`delta'
|
||
|
|
}
|
||
|
|
match_normal `obstype' `nobs' `nmis' `etaobs' `etamis' `yimp' `y'
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else { // draw
|
||
|
|
matrix `bstar'=e(b)
|
||
|
|
gen `u'=uniform()
|
||
|
|
if `normal' | `binary' {
|
||
|
|
matrix score `xb'=`bstar' if `touse'
|
||
|
|
if `normal' {
|
||
|
|
replace `yimp'=`xb'+e(rmse)*invnorm(`u')
|
||
|
|
}
|
||
|
|
else replace `yimp'=`u'<1/(1+exp(-`xb')) if !missing(`xb')
|
||
|
|
}
|
||
|
|
else { /* catcmd */
|
||
|
|
replace `yimp'=`cat'[1,1]
|
||
|
|
if "`cmd'"=="ologit" {
|
||
|
|
matrix score `xb'=`bstar' if `touse', forcezero
|
||
|
|
forvalues k=1/`cuts' {
|
||
|
|
* 1/(1+exp(-... is probability of being in category 1 or 2 or ... k
|
||
|
|
local cutpt=`bstar'[1, `k'+`colsofb'-`cuts']
|
||
|
|
replace `yimp'=`cat'[1,`k'+1] if `u'>1/(1+exp(-(`cutpt'-`xb')))
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else { /* mlogit */
|
||
|
|
* care needed dealing with different possible base categories
|
||
|
|
tempvar cusump sumexp
|
||
|
|
local basecat=e(basecat) /* actual basecategory chosen by Stata */
|
||
|
|
gen `sumexp'=0 if `touse'
|
||
|
|
forvalues i=1/`nclass' {
|
||
|
|
tempvar xb`i'
|
||
|
|
local thiscat=`cat'[1,`i']
|
||
|
|
if `thiscat'==`basecat' {
|
||
|
|
gen `xb`i''=0 if `touse'
|
||
|
|
}
|
||
|
|
else matrix score `xb`i''=`bstar' if `touse', equation(`thiscat')
|
||
|
|
replace `sumexp'=`sumexp' + exp(`xb`i'')
|
||
|
|
}
|
||
|
|
gen `cusump'=exp(`xb1')/`sumexp'
|
||
|
|
forvalues i=2/`nclass' {
|
||
|
|
replace `yimp'=`cat'[1,`i'] if `u'>`cusump'
|
||
|
|
replace `cusump'=`cusump'+exp(`xb`i'')/`sumexp'
|
||
|
|
replace `yimp'=. if missing(`xb`i'')
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
cap drop `gen'
|
||
|
|
rename `yimp' `gen'
|
||
|
|
*replace `gen'=`y' if `obstype'==1
|
||
|
|
replace `gen'=`y' if !missing(`y')
|
||
|
|
lab var `gen' "imputed from `y'"
|
||
|
|
}
|
||
|
|
di _n in ye `nmis' in gr " missing observations on `y' imputed from " /*
|
||
|
|
*/ in ye `nobs' in gr " complete observations."
|
||
|
|
end
|
||
|
|
|
||
|
|
program define match_normal
|
||
|
|
* Prediction matching, normal or binary case.
|
||
|
|
args obstype nobs nmis etaobs etamis yimp y
|
||
|
|
quietly {
|
||
|
|
* For each missing obs j, find index of observation
|
||
|
|
* whose etaobs is closest to etamis[j].
|
||
|
|
tempvar sumgt
|
||
|
|
tempname etamisi
|
||
|
|
gen long `sumgt'=.
|
||
|
|
* Sort etaobs within obstype
|
||
|
|
sort `obstype' `etaobs', stable
|
||
|
|
forvalues i=1/`nmis' {
|
||
|
|
local j=`i'+`nobs'
|
||
|
|
scalar `etamisi'=`etamis'[`j']
|
||
|
|
replace `sumgt'=sum((`etamisi'>`etaobs')) in 1/`nobs'
|
||
|
|
sum `sumgt', meanonly
|
||
|
|
local j1=r(max)
|
||
|
|
if `j1'==0 {
|
||
|
|
local index 1
|
||
|
|
local direction 1
|
||
|
|
}
|
||
|
|
else if `j1'==`nobs' {
|
||
|
|
local index `nobs'
|
||
|
|
local direction -1
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
local j2=`j1'+1
|
||
|
|
if (`etamisi'-`etaobs'[`j1'])<(`etaobs'[`j2']-`etamisi') {
|
||
|
|
local index `j1'
|
||
|
|
local direction -1
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
local index `j2'
|
||
|
|
local direction 1
|
||
|
|
}
|
||
|
|
}
|
||
|
|
* In case of tied etaobs values, add random offset to index in the appropriate direction
|
||
|
|
count if `obstype'==1 & reldif(`etaobs', `etaobs'[`index'])<1e-7 // counts as equality
|
||
|
|
scalar count`i'=r(N)
|
||
|
|
if r(N)>1 {
|
||
|
|
local index=`index'+`direction'*int(uniform()*r(N))
|
||
|
|
}
|
||
|
|
replace `yimp'=`y'[`index'] in `j'
|
||
|
|
}
|
||
|
|
}
|
||
|
|
end
|