COMPENSATING FOR WAVE NONRESPONSE IN THE 1979 ISDP RESEARCH PANEL

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1 COMPENSATING FOR WAVE NONRESPONSE IN THE 1979 ISDP RESEARCH PANEL 1. Introducton Graham Kalton, Unversty of Mchgan ames Lepkowsk, Unversty of Mchgan Tng-Kwong Ln. Natonal Unversty of Sngapore The choce between weghtng adjustments and mputaton for handlng mssng survey data s generally straghtforward: as a rule, weghtng adjustments are used for total nonresponse and mputaton s used for tem nonresponses. There are, however, several stuatons where the choce s debatable. In general, these are stuatons of what mght be termed partal nonresponse, where some data are collected for a sampled unt but a substantal amount of the data s mssng. These stuatons nclude cases where the respondent termnates the ntervew prematurely, where data are not obtaned for one or more members of an otherwse cooperatng household (for household level analyss), and where an ndvdual provdes data for some but not all waves of a panel survey. If weghtng s used for partal nonresponse, the avalable responses for that unt may be employed n the determnaton of the weghts, but the unt tself s dscarded, resultng n a loss of data. On the other hand, f mputaton s used, a szeable number of responses for a partally nonrespondng unt wll need to be mputed, gvng rse to concerns about the fabrcaton of much of the data and the effect of ths fabrcaton on the relatonshps between varables. Ths paper examnes the choce between weghtng and mputaton for handlng the partal nonresponse that occurs when a respondent fals to provde data on one or more waves of a panel survey. Kalton (1985) provdes further dscusson of the ssues nvolved n choosng between weghtng and mputaton t~ handle wave nonresponse, and Cox and Cohen (1985) report the results of an expermental nvestgaton of these alternatves n the Natonal Medcal Care Expendture Survey. The objectve of ths study s to provde evdence on the choce between weghtng and mputaton for handlng wave nonresponse n the Survey of Income and Program Partcpaton (SIPP). The SIPP s a panel survey n whch households are ntervewed every four months over a perod of about two-and-a-half years (Herrot and Kasprzyk, 1984). One major product of the SIPP wll be an annual fle combnng three waves of data, and the focus of the present study s on ths annual fle. Snce a longtudnal fle for the frst three waves of the frst SIPP panel s not yet avalable, the emprcal nvestgaton reported here s based on the frst three waves of the 1979 Income Survey Development Program (ISDP) Table 1 Person ResponseNonresponsc n the Frst Three. Waves of the 1979 ISDP Research Panel (Excludng Total Nonrespondents) Response (1) Pattern Nonresponse (0) % Total Number of persons 20,676 Research Panel, a large-scale panel survey that was conducted as part of the development, of the SIPP. All the results reported here relate only to orgnal sample persons aged 16 and over n the area frame part of the 1979 Research Panel sample: persons sampled from the specal lst frames and persons jonng the panel after the frst wave are excluded from all the analyses. In a three-wave panel there are eght dfferent patterns of responsenonresponse for the sampled unts. Denotng 1 as response and 0 as nonresponse, one of these patterns s 000, representng the nonrespondents to all three waves. The form of adjustment for these total nonrespondents s unproblematc, namely a weghtng adjustment, and hence they wll not be consdered further here. The dstrbuton for the other seven patterns for the 1979 Research Panel s gven n Table 1. The frst pattern n Table 1 represents those who responded on all three waves of the panel, whereas the other sx patterns represent those who faled to respond on one or two of the waves. The ssue under study s whether weghtng or mputaton should be used to handle each of these sx patterns. The next secton of the paper dscusses how weghtng adjustments mght be appled, and the followng one dscusses the use of mputaton. The fnal secton presents some concludng remarks. 2. Weghtng Adjustments for Wave Nonresponse The use of weghtng adjustments for partal nonresponse presents two addtonal complcatons beyond those that apply wth weghtng adjustments for total nonresponse. One results from the fact that there s a great deal more nformaton avalable about partal nonrespondents than about total nonrespondents. Often only a lmted amount of auxlary nformaton s avalable for total nonrespondents (such as the PSUs and strata n whch they are located), whereas for partal nonrespondents there s also the nformaton provded by the~ responses to the questons they have answered. The complcaton rased by these extra data s how they should be taken nto account n determnng the weghtng adjustments for partal nonrespondents. The second complcaton arses from the fact that surveys are subject to many dfferent forms of analyses. Some partal nonrespondents wll have provded all the data needed for certan analyses, and hence can be ncluded n them, but they wll nol have provded all the da~a needed for some other analyses. If all those provdng the requste data for a partacular analyss are ncluded n that analyss, dfferent analyses wll be based on dfferent subsets of the sample. Ths rases the complcaton that dfferent sets of weghts are needed accordng to what subset of the sample s ncluded n a partcular analyss. These two complcatons are dscussed n turn subsequently n relaton to handlng wave nonresponse by weghtng adjustments. As an llustraton of' the frst complcaton, consder the smple case of compensatng for the second wave nonrespondents n the 1979 Research Panel. The auxlary varables avalable for these partal nonrespondents are the desgn varables (PSUs and strata, etc.) and ther wave 1 responses. The am s to dscover whch, f any, of these varables are assocated wth response status at wave 2, and then to develop weghts to compensate for dfferental wave 2 response rates n dfferent parts of the sample. Wth the large number of" wave 1 response varables, the frst step n the analyss s to reduce those to be nvestgated n detal to a 372

2 manageable number. Ths was done by examnng the bvarate assocatons of each of the auxlary varables n turn wth the wave 2 response status varable. All but a few of the auxlary varables were found to have vrtually no assocaton wth wave 2 response status, and these varables were therefore excluded from the further analyses. The next step was to employ the remanng auxlary varables as jont predctors of wave 2 response status usng SEARCH analyses (Sonqust, Baker, and Morgan, 1973) and logstc regressons. Fgure 1 presents the results of a SEARCH analyss, one whch explans 2.3 per cent of the varaton n the wave 2 response status varable. Examnaton of ths tree dagram shows that 88 per cent of the sample falls n cells wth response rates between 87 and 92 per cent, and that 98 per cent falls n cells wth response rates between 83 and 92 per cent. Only three small cells have dstnctly lower response rates. In terms of weghtng adjustments, gvng the cell wth the 92 per cent response rate a weght of 1, the weghts for 88 per cent of the sample would be between 1 and 1.06 and for 98 per cent would be between 1 and The use of these weghts, wth ther slght varaton, would be unlkely to have any apprecable effects on analyses of the data. Fgure 1 Search analyss for wave 2 response status As an alternatve to the SEARCH analyss, logstc regresson analyses wth wave 2 response status as the dependent varable were also conducted. For one of these regressons, the ndependent varables from wave 1 were the reason for proxy ntervew (1), the recpency of nterest ncome (2), the amount of personal earnngs n month 2 (3), the relatonshp to the reference person (4), the type of famly (5), martal status (6), and the two-factor nteractons (1,2), (1,3), (1,4), (1,6), (4,5) and (5,6). Followng Lttle and Davd (1983}, the weghts for wave 2 respondents were then set to be the nverses of ther ndvdual predcted means from ths regresson. Fgure 2 shows the resultng dstrbuton of weghts. Ths dstrbuton has a smlar spread to that obtaned from the SEARCH analyss, but n ths case there are a few outlers. In praclce, these outlers would probably be trmmed back to avod the ncrease n samplng error assocated wth relatvely large weghts Fgure 2 Frequency dsfrbufon of nonresponse adusfmenf facfors from fhe logstc regresson model ~EARCH ANALYSIS: WAVE 2 RESPONSE STATUS t REF. PERSON N [ REF, PER, OTHER I N : ].378 N : IMARI TAL STATUS I PRESENT 1 WIDOWED 1 I NEVER ED I MARRIED REASON PROXY. ~,M I L TYPE [NOT PROXY~ I INCAPABLE, I I STUDENT' IDROPPED I TEMP. ABH SAMPLE, 7 OTHER I N : 1139 A N :.177 MONTH 2 INCOME NONE 91% N- 12OO2 INCOME SAVINGS ;REDIT UN N ~CCOUNTS \ 7 Eq YES NO AI! 92% 89% N~7879 N=4123 REF. OR RELATIVE 2.3% VARIATION EXPLAINED I NON- RELATIVE 92% 84% N = 7680 IN = 199 :> U (-- 0" o) ll,.,,'q I t 7 f1,,.--.,-"l I ct- v c7 f 7,q ~q 'qtq..,iq ~q'! qjq 'l.l tq'l lqjq 1"1jfl tq~l ~qvl] 7f 7f I.I Adjusfment focfor The results of the above analyses are farly reassurng about the nature of wave 2 nonresponse. Comparsons of wave 2 respondents and nonrespondents show that the two groups are generally very smlar n terms of ther wave 1 responses. The dfferences that have been dentfed are not major ones, and weghtng adjustments can be employed to compensate for them. Snce the varaton n these weghts s not, great, ther use wll not result n much loss of precson n the survey estmates. The weghts from the SEARCH analyss, tor example, would be lkely to lead to an ncrease of less than 12 per cent n the varance of the survey estmates. The second complcaton noted above concerns the need to employ dfferent sets of weghts for dfferent types of analyses n the presence of partal nonresponse. For nstance, consderng the patterns of wave nonresponse n Table 1, t can be seen that patterns 1, 2, 3 and 5 provde data for crosssectonal analyses of wave 1, patterns 1, 2, 4 and 6 provde data for cross-sectonal analyses of wave 2, patterns 1 and 2 provde data for analyses of changes between waves 1 and 2, and only pattern 1 provdes data for formng aggregates across all three waves (e.g., ncome over the perod). For any 373

3 partcular analyss, the respondents n the patterns that provde the requste data need to be weghted up to represent the other patterns. There are potentally seven combnatons of waves that could be used for dfferent forms of analyss, thus mplyng the need for seven dfferent sets of weghts. Wth more waves n the panel, the potental number of sets of weghts ncreases rapdly. For nstance, wth the eght waves from a full SIPP panel, there are 255 possble combnatons of waves, and hence as many as 255 dfferent sets of weghts could be requred. The number of sets of weghts needed would be reduced f not all the patterns of responsenonresponse occurred. In many panel surveys the major type of nonresponse s attrton nonresponse, whch refers to the stuaton n whch a unt drops out on one wave and remans out of the panel for all subsequent waves. If the only form of nonresponse was attrton nonresponse, there would be just four response nonresponse patterns for a three wave panel, namely 111, 110, 100 and 000, and only three sets of weghts would be needed. There would be one set of weghts for each wave: these weghts would apply straghtforwardly for cross-sectonal analyses of data from sngle waves, and an analyss ncorporatng data from two or more waves would use the weghts applcable to the latest wave nvolved n that analyss. Lttle and Davd (1983) propose a method for developng weghts to compensate for attrton nonresponse that attempts to take account of all the auxlary data avalable on the nonrespondents. The only nformaton known about nonrespondents at the frst wave (.e., the total nonrespondents) s ther values on the desgn varables (e.g., PSUs and strata), z; the nformaton avalable for those who drop out at the second wave comprses ther z-values and ther responses at the frst wave, Xl; the nformaton avalable for those who drop out at the thrd wave comprses ther z- and x 1- values and ther responses on the second wave, x2; and so on. Lttle and Davd propose runnng the followng seres of logstc or probt regressons wth the response ndcators r (r = I tor a respondent, r = 0 for a nonrespondent at wave ) as the dependent varables: (1) Regress r I on zl for the total sample (2) Regress r 2 on z 1 and x 1 for respondents at wave 1 (3) Regress r 3 on zl, x 1 and x 2 for respondents at wave 2; and so on. The nverses of the predcted means from these regressons then gve the weghts needed to compensate from one wave to the next. Let these weghts be denoted by Wl, w2.1, and w3.12. The overall weghts for frst wave respondents are then w l; for second wave respondents they are w 2 = wlw2.1; for thrd wave respondents they are w 3 = w2w3.12; and so on. Lttle and Davd (1983) also descrbe a weghtng scheme for nonattrton nonresponse, but the smplcty of the above procedure s lost, and ther scheme also has some unattractve features. As can be seen from Table 1, there were n fact a far number of nonattrton nonrespondents n the 1979 Research Panel: the patterns 101, 011 and 001 account for 6.0 per cent of the total sample and comprse almost one-thrd of the partal nonrespondents. An approach that can be used to avod the complcatons of the nonattrton nonresponse patterns s to convert them nto attrton patterns. Ths can be done ether by dscardng some waves of data, by mputng some waves of data, or by a combnaton of these procedures. Thus, for nstance, one mght mpute for the mssng wave n the 011 pattern, dscard the data n the 001 pattern, and ether mpute for the mddle wave or dscard the last wave n the 101 pattern. Note that f dscardng s the chosen soluton, the data need not have been collected n the frst place (except for ts potental use for methodologcal checks). 3. Imputng for Wave Nonresponse When wave nonresponse s handled by mputaton, all the mssng tems for a wave nonrespondent are assgned values, makng use of responses on other waves n dong so. As Kalton and Kasprzyk (1982) dscuss, the value mputed for the th nonrespondent on varable y may n general be expressed as Y =- f(xl, x2... Xp) + e, where f(x) s a functon of the p auxlary varables used n the mputaton, and e~ s an estmated resdual. If the e are set equal to zero. the mputaton scheme assgns the predcted means, and the scheme may be termed a determnstc one. On the other hand, f the e are estmated resduals, the scheme may be termed a stochastc one. Determnstc mputatons dstort the shape of the dstrbuton of y, and attenuate ts varance. For ths reason, stochastc mputaton schemes are generally preferred. In the SIPP and the 1979 ISDP Research Panel, n common wth most panel surveys, many of the same tems are repeated on each wave. Often the responses to a repeated tem are hghly consstent over tme, and when ths occurs the response on one wave can serve as a powerful auxlary varable to use for mputng the mssng response on another wave. To llustrate ths pont, we consder frst some categorcal varables and then some contnuous varables from the 1979 Research Panel. For the categorcal varables we examne the consstency of responses across the frst two waves of the 1979 Research Panel. The upper part of Table 2 presents unweghted crosswave dstrbutons of responses to whether the person worked n the quarter and to two recpency tems for orgnal sample persons aged 16 and over who responded on both waves. The lower part of the table gves correspondng dstrbutons of reasons for not workng for those who were not at work on both waves. As the frst row of the table shows, 58.2 per cent of persons reported that they worked on both waves and 34.5 per cent reported that they dd not work on ether wave. Thus, a total of 92.8 per cent of the respondents were consstent n ther responses across the frst two waves of the panel. Table 2 Dstrbuton of sample persons across Waves 1 and 2 for selected varables for orgnal sample respondents for both waves ages 16 and older from the area frame, 1979 ISDP Research Panel lstwave Yes Yes No No Conss- Sample Item 2nd wave Yes No Yes No tency sze Worked n quarter Recevng Soc. Sec Recevng Fed. SSI Reasons for not workng: Gong to school Ddn't want to work Retred , , , , , ,

4 The degree of consstency of response for all the tems n Table 2 s hgh, wth the lowest level of consstency beng 84.9 per cent for the responses to the tem "Ddn't want to work" as a reason for not workng. That the "Ddn't want to work" tem exhbts the lowest level of consstency s perhaps not unexpected, gven ts greater degree of subjectvty than the other tems. It s lkely that all these consstency measures are underestmates, because of measurement errors, possble msmatches of respondents across waves, and other reasons. Even tems lke race and martal status show some degree of nconsstency. The former tem has a consstency measure of 99.6 per cent, and the latter tem has one of 97.8 per cent; several of the nconsstences n martal status were n fact logcal mpossbltes, such as marred, wdowed or dvorced at wave 1 and never marred at wave 2. The hgh levels of consstency found n Table 2 suggest that the response to one of these tems on one wave s a good predctor for a mssng response on the other wave. In order to llustrate how the qualty of mputatons based on responses to the same tem on another wave may be assessed, consder the tem n the frst row of the table, whether the respondent worked n the quarter or not. Among the respondents to both waves, 94.4 per cent of those who answered "Yes" to ths tem at wave 1 (.e., sad they worked n the quarter) also sad "Yes" at wave 2, and 90.1 per cent of those who answered "No" at wave 1 also answered "No" at wave 2. There were 1518 persons who answered ths queston on wave 1, but faled to answer t on wave 2; of these, 922 answered "Yes" at wave and 596 answered "No". Usng a determnstc mputaton scheme, all those answerng "Yes" at wave 1 would be assgned "Yes" answers at wave 2 (ths beng the modal wave 2 response amongst, those answerng "Yes" at wave 1); smlarly, all those answerng "No" at wave 1 would be assgned "No" answers at wave 2. Assumng that nonrespondents at wave 2 are mssng at random condtonal on ther wave 1 responses, one can expect that 94.4 per cent of the 922 respondng "Yes" at wave 1 wll be correctly assgned "Yes" at wave 2 (.e., an expected 870 persons' and 90.1 percent of the 596 answerng "No" at wave 1 wll be correctly assgned "No" answers at wave 2 (.c.. an expected 537 persons). Thus ths mputaton scheme may be expected to correctly assgn the responses of 92.7 per cent of' the wave 2 nonrespondents. Wthout usng the wave 1 responses n the mputaton scheme, all the 1518 wave 2 nonrespondents would be assgned "Yes" responses wth a determnstc mputaton scheme, snce "Yes" s the modal answer among wave 2 respondents. Agan assumng wave 2 nonrespondents are mssng at random condtonal on ther wave 1 responses, an expected 61.2 per cent of them would be correctly assgned "Yes" responses for wave 2. The above determnstc scheme based on wave 1 responses suffers the dsadvantage that t mputes only 60.7 per cent of "Yes" wave 2 responses, whereas 61.2 per cent of "Yes" responses should be mputed to generate the correct dstrbuton of "Yes" and "No" answers under the mssng data model adopted. (The dfference here s small, but t could be greater n other cases.) In addton, the determnstc mputaton scheme leads to a greater stablty of responses over the two waves than s mpled by the model: there are no changes n responses from wave 1 to wave 2 for those wth mputed wave 2 responses. A stochastc mputaton scheme can avod these dsadvantages. A stochastc scheme for the above example would assgn "Yes" responses to 94.4 per cent of wave 2 nonrespondents who answered "Yes" at wave 1 and "No" responses to the other 5.6 per cent, and t would assgn "No" answers to 90.1 per cent of wave 2 nonrespondents who answered "No" at wave 1 and "Yes" answers to the other 9.9 per cent. A dsadvantage of the stochastc scheme, however, s that t reduces the qualty of the mputatons: based on the mssng at random condtonal on wave 1 response model, the expected percentage of correct mputatons wth ths scheme s only 86.6 per cent. It should be emphaszed that all the measures of the qualty of the mputatons are based on a model for the nonrespondents. The measures may be msleadng f the model fals to hold. The model used here assumes that the wave 2 nonrespondents have the same dstrbuton of wave 2 responses as the wave 2 respondents, condtonal on ther wave 1 responses. Thus, for nstance, t s estmated that 94.4 per cent of the wave 2 nonrespondents who answered "Yes" at wave 1 would answer "Yes" at wave 2. Ths estmate may be serously n error f the model s napproprate, and f so. the measures of mputaton qualty wll be nvald. Consder now the mputaton of contnuous varables across waves of a" panel survey. Kalton and Lepkowsk (1983) descrbe a varety of procedures that can be employed for crosswave mputaton n a two-wave panel, usng the value of a varable on one wave to mpute the mssng value of the same varable on another wave. The wdely used hot-deck mputaton procedure does not work well when the auxlary varable and the varable to be mputed are very hghly correlated, as wll often be the case wth crosswave mputaton. Wth the hot-deck procedure, the auxlary varable s categorzed nto cells, and an ndvdual wth a mssng value on the varable under consderaton s assgned the value of a respondent from the same cell. Thus an ndvdual from one end of a cell may be assgned the value from a respondent at the other end of that cell. Closer matches between nonrespondents and donors can be obtaned by ncreasng the number of hot-deck cells, but the number of cells has to be lmted to ensure that matches can be made. The categorzaton wth the hot-deck procedure can be avoded by usng some form of regresson mputaton. Consder, for example, the mputaton of the hourly rate of pay of ndvdual on wave 2 (Y) gven the ndvdual's hourly rate of pay on wave 1 (x). A smple regresson mputaton model s Y = a + bx + e, wheree saresdualterm. Thee'sdonot need to have a zero mean, and no restrcton need be placed on ther dstrbuton. Regresson mputaton can be vewed as constructng a new varable ) - a + bx~ for all ndvduals, mputng the e's for the nonrespondents, and then calculatng Y as Y + e- The e's may be assgned by any approprate mputaton scheme. They may, for nstance, be mputed by a hot-deck procedure, selectng respondents' e's wthn mputaton cells formed by, say, age, sex, and categorzed wave 1 hourly rate of pay to assgn to the nonrespondents. The choce of regresson mputaton model s not crtcal, snce the assgnment of the e's can protect aganst a msspecfed model. The better the choce of model, however, the smaller s the varance of the e's, and hence the better s the qualty of the mputed y's. Obvous choces for a and b are the least squares estmates obtaned from a regresson of respondents on both waves, but smpler alternatves may also work well. The smplest model s to take a - 0, b = 1, whch specfes the wave 2 value as the wave 1 value plus the change between waves: the mputaton s then made for changes. Other relatvely smple models set ether a = 0 or b = 0; the frst s a proportonate change model and the second an addtve change model. There s n fact no need to nclude the a term n the model, snce t can be ncorporated as part of the resdual (.e.. the resdual s taken to be a + el). The qualty of crosswave mputatons depends on (1) the correlaton between the values of the tem from one wave to the next and (2) the qualty of the mputatons for the resduals obtaned by usng other auxlary varables. We present some fndngs from the 1979 Research Panel relatng to the frst of these factors. Frst consder the hourly rate of pay varable. For orgnal sample respondents aged 16 and older n the area frame reportng hourly rate of pay on each of the frst two waves of the Panel, the correlaton between the two waves s Smlarly, from waves 2 to 3 the correlaton s and from waves 1 to 3 t s (All these correlatons are computed after 28 cases of apparent keyng errors had been removed.) 375

5 These hgh correlatons suggest that f a person's hourly rate of pay s avalable for one wave but not for a neghborng wave, the mssng rate can be mputed wth lttle error (even before consderng the use of auxlary varables n the mputaton of the resdual term). Unlke hourly rate of pay, most of the amounts tems n the 1979 Research Panel were reported on a monthly bass, so that there are three amounts reported for each wave. The cross-month correlatons for one amount tem, wage and salary ncome, for the frst three waves of the 1979 Research Panel are gven n Table 3. The data are agan lmted to orgnal sample persons aged 16 and older from the area sample, and only persons reportng that they receved wage and salary ncome are ncluded n the correlaton estmates. The correlatons were computed usng a parwse mssng data deleton algorthm so that the numbers of records used for dfferent correlatons may vary. Several records n the data fle had apparent keyng errors for the wage and salary amount (e.g., the amount ncreased from one month to the next exactly by a factor of 10 or 100, suggestng a decmal place shft n the keyng process). Snce these potental errors substantally reduced cross-month correlatons, the data values n error were excluded from the parwse correlatons. Table 3 Cross-month correlatons for wage and salary ncome amount for orgnal sample persons ages 16 and older from the area frame, 1979 ISDP Research Panel The correlatons across months are generally hgh, rangng from to The hghest correlatons are between months wthn waves, whle the lowest tend to occur for months that are more than 6 months apart. Lookng down the man dagonal of the lower trangular matrx n Table 3, t can be seen that correlatons between adjacent months n dfferent waves are lower than those between adjacent months n the same wave. There are several possble explanatons. One s that respondents tend to gve falsely consstent responses wthn a wave, leadng to unduly hgh wthn wave correlatons. It seems more lkely, however, that t s the between wave correlatons that are too low. Ths could arse because of response varaton between waves, ncludng cases of proxy reports on one wave and self-reports on another. Also, a close examnaton of the records suggests that there may be some msmatched records n the fle, gvng rse to large dfferences n wage and salary ncome between waves. Correlatons for other amounts tems n the 1979 Research Panel demonstrate smlar hgh cross-month correlatons. The correlatons for wage and salary ncome and sx other amounts tems are summarzed n Table 4. Average correlatons were computed for the same dfference between months, and separately for reports wthn the same wave and between dfferent waves. For example, the average wthn wave correlaton for a one month dfference for the wage and salary amount s the average of months 1 and 2. months 2 and 3, months 4 and 5, months 5 and 6, months 7 and 8, and months 8 and 9 correlatons from Table 3. The correspondng average between wave correlaton s the average of the months 3 and 4 and months 6 and 7 correlatons. As observed for wage and salary ncome amounts, the average correlatons between months n dfferent waves for the other tems are always smaller than those between months n the same wave. The correlatons also decrease as the number of months between reports ncreases. But generally the correlatons for these ncome tems are hgh, ndcatng the knd of stablty that may be used to provde accurate mputed values for mssng data by usng cross-month and cross-wave mputaton strateges. Table 4 Average cross-month correlatons for seven amount tems for orgnal sample persons ages 16 and older from the area sample, 1979 ISDP Research Panel 1 One month dfference Two month dfference Wthn Wthn Between and wave wave Between Wthn wave Between wave Wthn and Three Four Fve Sx Seven Eght Between month month month month month month,, Wage and salary amount Personal earnngs Socal Securty ! Federal SSI AFDC Unemployment =ompensaton I_ ! Food stamps Excludng apparent keyng errors as mssng data. 376

6 One of the tems n the table has apprecably lower correlatons than the rest, namely unemployment compensaton amounts. The correlatons for ths tem start by fallng as the number of months between reports ncreases, but then rse for longer ntervals: the correlatons for months sx or more months apart are n fact hgher than the correlaton for one month apart. Ths pattern of correlatons may ndcate that short-term unemployment receves unstable compensaton whle longer-term employment receves relatvely stable amounts of compensaton. In any case, the lower correlatons for ths tem ndcates the need for greater efforts to employ effectve auxlary varables n mputng for the resduals for unemployment compensaton. The precedng dscusson has been n terms of two waves of data, one of whch s mssng. In a three-wave panel, the wave nonresponse patterns are 110, 101, 011, 100, 010 and 001. Wth pattern 110, the mssng thrd wave data could be forecast from the second wave by one of the procedures dscussed; t would probably be satsfactory to gnore the frst wave data, snce they are unlkely to add much explanatory power to that gven by the second wave data alone. In the same way, wth 011, the frst wave data could be backcast from the second wave data. The mssng frst and thrd waves of data n the pattern 010 could be backcast and forecast respectvely. The second wave's data n 100 and 001 could smlarly be forecast and backcast, but the other mssng waves are two waves apart: these could equally be mputed by one of the precedng procedures, but probably less well. The fnal pattern, 101, has the mssng wave surrounded by nonmssng waves. In ths case, t should be possble to develop a stronger mputaton method, usng both adjacent waves' data n the mputaton scheme. The mputaton schemes descrbed above use the response for a varable on one wave n mputng for a mssng response to that varable on another wave. These schemes are especally effectve when the varable s hghly stable, or at least the values are hghly correlated between waves, for then the observed value on one wave s a powerful predctor of the mssng value on the other. A lmtaton to these schemes s that the value of the same varable on another wave must be avalable. Kalton and Lepkowsk (1983) found that n many cases these schemes could not. be used n mputng for hourly rate of pay n the 1979 Research Panel because a person wth a mssng hourly rate of pay on one wave also had a mssng rate on the other wave, or was a non-wage earner or not part of the panel on the other wave. An alternatve back-up mputaton procedure s needed to deal wth such cases, addng to the complexty of the mputatons and lowerng ther overall qualty. Another stuaton gvng rse to responses to the tem beng unavalable on another wave s when the tem was ncluded on the questonnare for only one wave. The so-called "topcal modules" on the SIPP questonnares fall nto ths category. When crosswave mputaton based on the same tem on another wave cannot be appled, other forms of crosswave mputaton, usng other varables, may be employed. However, the qualty of the resultant mputatons wll rarely compare wth that of crosswave mputatons based on the same tem. If mputaton s used to handle wave nonresponse, the possblty of collectng data on addtonal auxlary varables to mprove the predctve power of the mputaton models s worth consderng. In partcular, f a unt s a nonrespondent on one wave, addtonal data may be collected at the next wave. Such a strategy s beng adopted n the SIPP, wth the addton of a "Mssng Wave" secton to the questonnare for the fourth and subsequent waves of data collecton (Baley, Chapman and Kasprzyk, 1985). Ths secton collects nformaton on labor force partcpaton, ncome sources and asset ownershp nonownershp of respondents who, although elgble, dd not respond to the precedng wave. 4. Concludng Remarks The choce between weghtng adjustments and mputaton for handlng wave nonresponse s not a smple one. Each method has ts advantages and dsadvantages. Imputaton creates a completed data set that s easy for the analyst to use and, when based on a model wth hgh predctve power, mputaton s more effcent than weghtng. The development of good mputatons for all the varables n a mssng wave s, however, a major undertakng. Unless the overall mputaton scheme s constructed wth great care, takng account of the cross-sectonal and longtudnal nterrelatonshps between all the varables, nconsstent or otherwse unacceptable mputed values may be ass~oned. In any event, mputaton fabrcates data to some extent and t wll cause an attenuaton n some of the covarances between varables. The amount of fabrcaton and attenuaton s slght when powerful crosswave mputaton models are used, but such models cannot be used n all cases. On the other" hand, whle weghtng avods the attenuaton problem, the need to use dfferent sets of weghts for dfferent types of analyses creates complextes for the analyst and can lead to nconsstent results. Wth both mputaton and weghtng havng ther advantages and dsadvantages, t may be that some combnaton of the two methods, such as that outlned at the end of Secton 2, s the best soluton. References Baley, L., Chapman, D.W. and Kasprzyk, D. (1985). Nonresponse adjustment procedures at the Census Bureau: a revew. Proceedngs of the Bureau of the Census Frst Annual Research Conference, Cox, B.G. and Cohen, S.B. (1985). Methodologcal Issues for Health Care Surveys. New York: Marcel Dekker. Herrot, R.A. and Kasprzyk, D. (1984). The Survey of Income and Program Partcpaton. Proceedngs of the Socal Statstcs Secton, Amercan Statstcal Assocaton, Kalton, G. (1985). Handlng wave nonresponse n longtudnal surveys. Proceedngs of the Bureau of the Census Frst Annual Research Conference, Kalton, G. and Kasprzyk, D. (1982). Imputng for mssng survey responses. Proceedngs of the Secton on Survey Research Methods, Amercan Statstcal Assocaton, Kalton, G. and Lepkowsk,. (1985). Followng rules n the Survey of Income and Program Partcpaton. ournal of Economc and Socal Measurement, 1, (forthcomng). Kalton, G. and Lepkowsk,. (1983). Cross-wave tem mputaton. In Techncal, Conceptual, and Admnstratve Lessons of the Income Survey Development Program (ISDP), M. Davd, ed., pp New York: Socal Scence Research Councl. Kasprzyk, D. and Kalton, G. (1983). Longtudnal weghtng n the Income Survey Development Program. In Techncal, Conceptual, and Admnstratve Lessons of the Income Survey Development Program (ISDP), M. Davd, ed., pp New York: Socal Scence Research Councl. Lttle, R. and Davd, M. (1983). Weghtng adjustments for non-response n panel surveys. Bureau of the Census workng paper. Sonqust,.A., Baker, E.L., and Morgan,.N. (1973). Searchng for Structure. Ann Arbor, Mchgan: Insttute for Socal Research. 377

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