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Correcting for Selective Nonresponse in the National Longitudinal Survey of Youth Using Multiple Imputation.

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Title: Correcting for Selective Nonresponse in the National Longitudinal Survey of Youth Using Multiple Imputation.
Language: English
Authors: Davey, Adam, Shanahan, Michael J., Schafer, Joseph L.
Source: Journal of Human Resources. Sum 2001 36(3):500-519.
Peer Reviewed: Y
Page Count: 20
Publication Date: 2001
Document Type: Journal Articles
Reports - Research
Descriptors: Family Characteristics, Longitudinal Studies, Research Problems, Statistical Bias
Assessment and Survey Identifiers: National Longitudinal Survey of Youth
ISSN: 0022-166X
Abstract: Principal components analysis revealed four patterns of nonresponse on children's psychosocial adjustment, lifetime poverty experiences, and family history. Results from examining latent growth curve models using listwise deletion and multiple imputation indicated that multiple imputation corrected for selective nonresponse, providing less-biased estimates and standard errors. (Contains 18 references.) (SK)
Entry Date: 2002
Accession Number: EJ628925
Database: ERIC
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  Value: <anid>AN0005530494;JHR01JUN.01;2001Dec10.13:41;v6.0.1</anid> <title id="AN0005530494-1">CORRECTING FOR SELECTIVE NONRESPONSE IN THE NATIONAL LONGITUDINAL SURVEY OF YOUTH USING MULTIPLE IMPUTATION </title> <hd id="AN0005530494-2"> ABSTRACT </hd> <p>Survey attrition and nonresponse, particularly when selective, present unique challenges to researchers interested in studying developmental processes and longitudinal change. Four distinct patterns of nonresponse on children's psychosocial adjustment and lifetime poverty experiences and family histories are identified using principal components analysis. In turn, membership in these four groups is significantly predicted by the child's demographic characteristics, family experiences, and previous values on adjustment variables, indicating selective nonresponse and raising the possibility of biased estimates based on listwise deletion of missing data. We then examine a set of latent growth curve models that interrelate children's family experiences and psychosocial adjustment using list-wise deletion (LD) and multiple imputation (MI) procedures. Implications for treatment of nonresponse in national longitudinal surveys are discussed. </p> <hd id="AN0005530494-3"> I. Introduction </hd> <p>A growing number of national data sets incorporate longitudinal components. These include, for example, the Panel Study of Income Dynamics, the Health and Retirement Survey, the National Survey of Families and Households, and the National Longitudinal Surveys. Greater availability of longitudinal data presents new opportunities for researchers to address questions about human development and longitudinal change, but it also poses potential challenges, particularly due to sample attrition and selective nonresponse. Failure to deal with missing data results in a loss of statistical power because partially complete cases typically are discarded from the analysis. Also, when one or more systematic processes are responsible for the pattern of missing and observed data (as is often the case), parameter estimates will be biased (compare with Little and Rubin 1987, Schafer 1997). </p> <p>Indeed, problems associated with missing data are of general concern to social scientists and are the subject of growing interest and attention (for example, Allison 1987; Little and Rubin 1987, 1989; Rubin 1987; Schafer 1997). These problems are particularly acute with regard to longitudinal data (Little 1995, Schafer 1997) and when questions pertain to the study of developmental processes, because these methods require use of data from multiple waves simultaneously, and inferences about individuals over a period of time rather than at a single point in time. However, the few studies that have examined the role of attrition in longitudinal studies have typically reported relatively small or inconsistent biases in estimates, despite considerable evidence for selective nonresponse (for example, Burkham and Lee 1998; Fitzgerald, Gottschalk, and Moffitt 1998). Most commonly, sampling or attrition weights are applied to longitudinal data in order to begin correcting for the selective processes which tend to render longitudinal data sets less representative of the original study population with successive waves of data. In the NLSY, for example, population-based weights are available in each wave in order to make the data set representative of the population at that point in time. It is less clear, however, how corrections should be made when multiple waves of data are combined to investigate developmental change rather than status at a single point in time. From a developmental perspective, the initial sample is the one about which we wish to generalize regarding longitudinal change. Individuals with extreme trajectories (for example, most rapid increase of problem behaviors) or pathways (for example, most dynamic poverty experiences), however, may be most likely to drop from the study as a result of geographic mobility, multiple family changes, or extreme poverty. Indeed, bias due to selective attrition represents a distinct possibility in the contexts of many substantive interests. For example, what is the probability of educational continuation given frequent geographic relocations? Of pregnancy given family changes over time? Of early poverty experiences on subsequent employment? </p> <p>Using six years of longitudinal data from children of the National Longitudinal Survey of Youth (NLSY) sample, we examined the association between lifetime poverty trajectories and children's psychosocial adjustment, comparing traditional listwise deletion of cases with missing data and multiple imputation, which makes use of all available information. Results across methods lead to different substantive conclusions as a result of selective nonresponse processes that we identify in the data. </p> <hd id="AN0005530494-4"> A. Brief Introduction to Missing Data </hd> <p>In their seminal work on the analysis of incomplete data, Little and Rubin (1987) distinguish between two types of ignorably missing data. Data that are missing completely at random (MCAR) depend neither on the values of the observed data nor on the values of the missing data. Thus, MCAR data are equivalent to a simple random sample of the full data set. </p> <p>However, it is typically unrealistic to assume that data are MCAR (for exceptions, see Graham, Cumsille, and Taylor 2001). Rather, under many circumstances, there may be selective processes which determine whether a particular value is observed or missing. For example, individuals with extremely high incomes may be reluctant to report income information. Similarly, individuals who are geographically mobile may be difficult to track and retain in a longitudinal study. A more realistic assumption under these circumstances is that data are missing at random (MAR), that the values of the missing data depend only on (that is, can be completely explained by) information in the observed data. Under these circumstances, the mechanism that determines whether a particular value is observed or missing is said to be "ignorable." </p> <p>Although it is possible to test whether data are MCAR, it is not possible to test whether the data are MAR because to do so would require further information about the unobserved data. Even when the data are not strictly MAR this assumption will often represent a reasonable approximation (see Little and Rubin 1987, Schafer 1997 for a more thorough explication of data which are MAR), and is less stringent than the assumption that data are MCAR. Thus, any attempt to identify and correct for selective nonresponse will represent an improvement in the accuracy of results over making no attempt at all. </p> <hd id="AN0005530494-5"> B. Methods for Dealing with Missing Data </hd> <p>Numerous methods are available for dealing with missing data, each with strengths and limitations. Below, we consider four commonly employed techniques, high-lighting the relevant characteristics of each. </p> <p>I. Listwise Deletion </p> <p>Listwise deletion -- the removal of cases which are missing one or more data points -- is by far the most commonly employed method for dealing with missing data. This approach is valid for point estimates only when the data are MCAR but will otherwise lead to biased estimates. For confidence intervals, however, listwise deletion is always inefficient, because information from partially observed cases is discarded. Thus the listwise deletion approach to missing data is easy to implement, but can yield seriously misleading estimates. Further, in the present context, use of listwise deletion results in loss of more than half of the sample (some due to dropout, some due to nonresponse within survey waves), making methods for dealing with incomplete data preferable for reasons of both statistical power and correcting bias in parameter estimates and confidence intervals. More sophisticated techniques which are useful when data are MCAR or MAR are discussed below. </p> <p>2. Full Information Maximum Likelihood (FIML) </p> <p>The idea behind FIML originates with Anderson (1957), who discovered that, under nested missing data structures (for example, when individuals who are missing at one wave of data collection are missing at all subsequent waves), the resulting likelihood function could be factored separately for each pattern of missing data. The EM (expectation-maximization) algorithm (Dempster, Laird, and Rubin 1977) allowed for solving otherwise intractable problems (that is, where no closed-form solution exists or would be exceedingly difficult to specify or solve) via iterative methods, and was largely responsible for the widespread application of Anderson's methods. Initial estimates of model parameters (based, for example, on estimates from listwise or pairwise deletion) are optimized over all available information from complete and partial cases. These new estimates are then substituted back in for the model parameters, and the optimization process continues in this fashion until the parameter estimates converge. Recently, this approach has been incorporated into statistical software packages such as AMOS (Arbuckle 1995; Wothke 1998). Even when data are only MAR, FIML makes use of all available data, even that from partially missing cases, and will provide valid point estimates and confidence intervals for population parameters. However, because it is a model-based technique, rather than a data-based technique, estimates of the same parameters and their confidence intervals may vary from analysis to analysis. </p> <p>3. Single Imputation. </p> <p>Single imputation is another technique useful when data are MAR, and involves replacing missing data with plausible values, which can be derived in any of a number of ways (for example, substitution of values from a complete case with similar values on the observed variables, or more sophisticated Bayesian methods). The result is a rectangular data matrix that is amenable to analysis with standard statistical software and parameter estimates will be consistent from one model to another. A single imputation will provide valid point estimates, but the associated standard errors will be too small. The imputation process naturally involves some uncertainty about what the unobserved value was, but this uncertainty is not reflected anywhere in the data matrix. As a result, this technique, like mean or regression substitution, leads to an overestimate of the precision of one's results. Multiple imputation, discussed next, represents one way of correcting for the uncertainty inherent in the process of imputation. </p> <p>4. Multiple Imputation (MI) </p> <p>For both MAR and MCAR data, multiple imputation combines the strengths of FIML and single imputation in that it provides valid point estimates and confidence intervals along with a collection of rectangular data matrices that can be used for the analysis of many different models. In addition, the fact that missing data are replaced with multiple plausible values provides the analyst with valid confidence intervals in the following fashion. Within any data set, there will always be some uncertainty about population parameters due to sampling variability. With incomplete data, some uncertainty is also introduced through the process of imputation. When multiple data sets are imputed, however, the only source of variability in parameter estimates across them is due to uncertainty from the imputation process (because the complete data components are identical across data sets). Thus, by decomposing the total variability in parameter estimates into within-imputation variability and between-imputation variability, the results can be accurately corrected for the uncertainty introduced through the imputation process. Schafer has recently written a software package, NORM, to perform multiple imputation and form valid inferences (described in Schafer 1997) under a normal model, making this technique readily available to social scientists without the technical expertise to implement MI themselves (other imputation models now becoming available are useful for categorical and mixedmodels). This is a highly generalized approach to missingness that can be used in conjunction with many statistical procedures, including, for example, structural equation models and logistic regression equations. </p> <p>In this paper we consider (<reflink idref="bib1" id="ref1">1</reflink>) the assessment of missingness problems in longitudinal data, (<reflink idref="bib2" id="ref2">2</reflink>) the assumptions of various strategies to correct for missingness, and (<reflink idref="bib3" id="ref3">3</reflink>) results based on alternative procedures for handling missing data. We conclude by considering strategies to minimize biases due to selective attrition in on-going national data collection efforts. </p> <hd id="AN0005530494-6"> II. Methods </hd> <hd id="AN0005530494-7"> A. Data </hd> <p>The National Longitudinal Survey of Youth (NLSY) is a nationally representative sample of 12,686 young men and women aged 14 to 22 in 1979 (Center for Human Resources 1995). Our research draws on data from the women who have been interviewed annually since 1979. The present study draws on data extending from the child's birth to 1992. These data include oversamples of African Americans, Hispanics, and poor non-Hispanic Whites.[<reflink idref="bib2" id="ref4">2</reflink>] </p> <p>Beginning in 1986, when the women were aged 21 to 28, assessments were conducted to assess their children's psychosocial adjustment. Children born to interviewed mothers originally numbered 5,255. Child assessments, based on interviews with mothers, have been completed biennially since 1986. We focus on children who were between four and six years of age in 1986 (N = 1,651). Characteristics of the children are shown in Table 1. </p> <hd id="AN0005530494-8"> B. Measures </hd> <p>1. Psychosocial Adjustment </p> <p>Since 1986. children have been assessed with the Behavior Problems Index (BPI). The BPI is a modification of Achenbach and Edelbrock's (1981) Behavior Problems Checklist created by Zill and Peterson (Baker et al. 1993). We focus on two prominent indicators of children's internalizing and externalizing symptoms, anxiety/depression and antisocial behavior. The anxiety/depression scale consists of five items measuring how often the child feels or complains that no one loves him or her, feels worthless or inferior, is unhappy, sad, or depressed, has sudden changes in mood, and is too fearful or anxious. The antisocial scale consists of four items measuring how often the child cheats or tells lies, bullies or is cruel to others, does not seem to feel sorry after he/she misbehaves, and breaks things on purpose or deliberately destroys his or her things or another's things. For both scales, mothers rated their child on a three point ordinal scale (1 = none of the time, 2 = some of the time, 3 = all of the time). </p> <p>In order to model change in these constructs across four waves of repeated measures, it is first necessary to determine that they are factorially invariant at least to the level of metric invariance (that is, that the indicators of antisocial behavior and anxiety-depression have the same relationship to the latent construct through time; compare with Meredith 1993). Preliminary analyses indicated that not all items were invariant over time, and these items were deleted from further consideration. For antisocial behavior, I deleted "breaks things on purpose"; for anxiety-depression I deleted "sudden mood changes" and "too fearful." I created scales as the average of retained items. </p> <p>2. Family Experiences </p> <p>Income data were used to create variables reflecting duration and transitions into and out of poverty. Poverty duration reflects the proportion of years spent in poverty by the child. Past duration refers to the proportion of years in poverty from birth to 1986, and current duration reflects proportion of years in poverty between 1986 and 1992. Transitions are also measured as the proportion of years in which a transition into poverty occurred. Past transitions refer to the number of times a household fell below the poverty line for its household composition prior to 1986, and current transitions refer to the number of times the household income fell below the poverty line between 1986 and 1992. Other variables included were the mother's age at the child's birth, years of maternal education, whether the mother was ever divorced, and whether the mother was never married. Interaction variables were created to reflect all eight combinations of race (African American and Hispanic, with non-Hispanic White as the reference category) and poverty experience (past duration, past transitions, current duration, current transitions). </p> <hd id="AN0005530494-9"> C. Statistical Model </hd> <p>Recent years have seen a rapid increase in the popularity of growth curve models (for example, Shanahan, Davey, and Brooks 1998; Willett and Sayer 1994, 1996) for the study of developmental processes. These models consist of a baseline model of growth, and predictors of the parameters of growth. Preliminary analyses indicated that for both antisocial and anxious/depressed behaviors, growth was best represented by a model in which each individual's observation at a given time was a function of the square root of time: Y<subs>it</subs> = pi<subs>0i</subs> + pi<subs>1i</subs> Square root of time + e<subs>it</subs>. In turn, the parameters of growth themselves (that is, an initial status, or "level," parameter and a rate of change, or "shape," parameter) are predicted by characteristics of the individual: pi<subs>0i</subs> = beta<subs>00</subs> + (Poverty) + u<subs>0i</subs>. </p> <hd id="AN0005530494-10"> D. Procedures </hd> <p>Following Rubin (1987), we used multiple imputation (MI) to construct 10 complete data sets using methods outlined by Schafer (1997) and implemented with his NORM software. Beginning with EM estimates (Dempster, Laird, and Rubin 1977), we augmented the data to construct posterior distributions for missing data. Independent draws[<reflink idref="bib3" id="ref5">3</reflink>] were performed every 1,000 iterations (to avoid autocorrelations) and values for missing data were imputed to create 10 complete data sets containing the dependent variable composites (that is, antisocial behavior and anxiety-depression) for 1986 1988 1990, and 1992, as well as their potential predictors. These ten data sets were created separately for each of the two dependent variables (antisocial behavior and anxiety-depression) for a total of 20 imputed data sets. Each of these data files was then analyzed separately. Parameter estimates from each analysis were combined through the process of multiple imputation inference to obtain the results presented in this article. </p> <p>Specially, multiple imputation partitions observed variance into within-imputation and between-imputation components. Total variance is calculated as </p> <p>[Multiple line equation(s) cannot be represented in ASCII text] </p> <p>where m is the number of imputed data sets, U is the simple average of complete-data variance estimates, and the between imputation variance is calculated as </p> <p>[Multiple line equation(s) cannot be represented in ASCII text] </p> <p>where Q<sups>(t)</sups> is the complete-data point estimate, and Q is the simple average of complete-data point estimates. Based on these values, a confidence interval can then be constructed as </p> <p>[Multiple line equation(s) cannot be represented in ASCII text </p> <p>Degrees of freedom for this interval are estimated as </p> <p>[Multiple line equation(s) cannot be represented in ASCII text </p> <p>Thus, the process of imputing multiple times allows for estimating uncertainty in the results due to incomplete data. </p> <p>Whereas it is a relatively straightforward matter to construct point estimates and confidence intervals for model parameters, it is a far more complex task to do the same with indices of model fit, such as chi-square estimates. Meng and Rubin (1992) present one method for comparing likelihood-ratio tests, but these techniques have not yet been implemented in the context of structural equation modeling. </p> <p>Two additional methodological issues must also be addressed before proceeding to discussing our results: assumptions regarding the multivariate normality of data, and complex sampling design of the NLSY. Regarding the former issue, imputations were made under a multivariate normal model, however our data contained variables that were dichotomous, ordinal, or nonnormally distributed. Thus, as with most applications of multiple imputation, our model used to generate the imputations is only approximately true. While less than optimal, simulation results suggest that multiple imputation is quite robust to departures from the imputation model (for example, Ezzati-Rice et al., 1995; Schafer 1997; Schafer and Olsen 1998). Recently, Schafer has developed software which can be used to impute categorical data under a log-linear model, combinations of continuous and categorical data under the general location model, and nested data under a mixed model, although this latter software can presently only accommodate two-level data, as opposed to the complex structure of occasions nested within individuals nested within complex survey design. There is a risk, then, that the standard errors of the parameters in our growth curve models presented below are too small (and hence that test statistics are too large). Under general circumstances, however, adjustments may be made by explicitly modeling this nested structure in order to correct standard errors according to a variety of standard methods (for example, multilevel models, generalized estimating equations, jackknife methods, etc.). </p> <p>Our first analyses were directed toward identifying patterns of missing data in the NLSY between 1986 and 1992. To address this issue, we begin by examining the extent to which missing/observed status on study variables can be reduced via factor analysis to a smaller subset of variables tending to be missing/observed together. Evidence for missing data mechanisms suggests (a) that nonresponse is at least somewhat selective, suggesting that parameter estimates may be biased if corrections are not made, and (b) that the data are at least partially MAR and that at least some variables included in our models are serving to make these corrections. Mechanisms for selective attrition are then examined by means of a series of logistic regression analyses, predicting missing status on each pattern of missing data we identify. Finally, we compare the results of analyses based on listwise-deleted and multiply imputed data. This comparison permits us to evaluate the extent to which our parameter estimates would be biased had we not corrected for missing data, and to reach more valid substantive conclusions about the developmental processes of primary interest. </p> <hd id="AN0005530494-11"> III. Results </hd> <hd id="AN0005530494-12"> A. Patterning of Missingness in the NLSY </hd> <p>To determine how many unique patterns of missingness were present in the NLSY, we used principal components analysis on all study variables (recoded for these analyses as 0 = observed and 1 = missing) which had at least some nonresponse. Because the missing/observed status of all variables is known, this analysis included all 1,651 observations. This included 20 BPI variables (from Antisocial, Anxious/Depressed, Dependent, Headstrong, and Hyperactive scales), past and current poverty durations and transitions, mother's education, ever divorced, and never married. A four-factor solution accounted for 84 percent of the variance and yielded a clearly interpretable pattern of factor loadings. After oblique rotation (patterns of missing data are expected to correlate in longitudinal research), the factors were clearly interpretable as: Missing at Time 1 (any of the five BPI subscales at Time 1: 339 cases), Missing at Time 2 (any of the five BPI subscales at Time 2: 174 cases), Missing at Times 3 and/or 4 and/or demographic variables (any of the five BPI subscales at Times 3 or 4, mother never married, mother ever divorced, or current poverty experiences: 657 cases), and Missing on Mother's Education and Past Poverty Experiences (mother's education or past poverty experiences: 68 cases; this pattern of missingness was not pursued further). </p> <p>Missingness on Time 1 BPI variables was not correlated with missingness at any other time point. The remaining three patterns of missing data were modestly intercorrelated, however, suggesting that nonresponse is associated with subsequent nonresponse and that the NLSY sample can be expected to become less representative of the original population over time, which would pose potential problems for the study of development questions. In sum, we find clear evidence for interpretable patterning of nonresponse in the NLSY data (that is, around time of measurement). We next proceed to examine predictors of missing status on each of these patterns of nonresponse as evidence for selective processes leading to bias if left unaddressed. </p> <hd id="AN0005530494-13"> B. Examining Mechanisms of Selective Attrition </hd> <p>A series of logistic regression models was estimated to predict missingness on three of the four patterns of missing data (Table 2) from information collected contemporaneously and from previous waves. A range of demographic variables, as well as dynamic descriptions of family experiences were selected as predictors of missing status, as well as prior levels of behavior problems (when predicting missing status beyond Time 1). These variables were expected to be most strongly predictive of selective nonresponse in the present context. Missingness at Time 1 was only predicted by mother's age at child's birth, with each additional year of mother's age being associated with a 17 percent greater probability (b = 0.16) that Time 1 BPI data would be missing. </p> <p>Missing status at Time 2 appeared to be far more systematic. Data from girls were only two-thirds as likely (b = -0.40) to be missing as data from boys at Time 2. Past poverty duration was associated with a greater probability of missing data. Those who had spent their entire lives in poverty by 1986 were more than 4.5 times more likely to be missing Time 2 data (b = 1.51) than those who had never experienced poverty. Interestingly, transitions into poverty had precisely the opposite relationship to missing status. Each transition into poverty over the same time period was associated with approximately 47 percent the likelihood (b = -3.74) that a child would be missing data at Time 2, compared with children who experienced no transitions into poverty (and were thus either chronically poor or never poor). This finding suggests that transient experiences with poverty may be less destabilizing than chronic poverty spells. Mother's marital status was also an important predictor. Those whose mothers were ever divorced were 2.25 times more likely (b = 0.81) than those whose mothers had not divorced to be missing data at Time 2, possibly reflecting an increased likelihood of geographic mobility. There was also evidence that children's initial psychosocial adjustment was important in predicting later study participation. Children with initially higher anxiety/depression scores were more likely (b = 0.22) than those with lower anxiety/depression to have missing data at Time 2. The effects of headstrong behavior were exactly the opposite, such that those who were more headstrong were less likely (b = - 1.59) to be nonresponders at Time 2. As with nonresponse at Time 1, data were more likely to be missing at Time 2 when mothers were older, with each year of mother's age associated with a 15 percent greater probability (b = 0.14) of nonresponse. </p> <p>Finally, the effects of poverty history interacted with race. There were significant interactions between being African American and past durations and transitions into poverty (b = - 1.59), and between being Hispanic and past transitions into poverty (b = 7.77). For those without any poverty experiences, there were very few differences between groups. For example, Hispanics were only 7 percent, and African Americans only 14 percent more likely than Whites to be nonresponders at Time 2. At the sample average levels of poverty duration, however, different results emerge. Whites spending 38 percent of their lives in poverty were 77 percent more likely to be nonresponders than those without any poverty experiences. Hispanics who had spent a similar proportion of their lives in poverty were only 8 percent more likely to be nonresponders, however, and African Americans only 10 percent more likely to be nonresponders. These effects were further magnified by comparing the three groups when they had spent their entire lives in poverty. Relative to Whites without any poverty experiences, the respective odds ratios for Whites, Hispanics, and African Americans were 4.52, 1.70, and 1.05. Thus, at high levels of poverty, Hispanics were only 38 percent as likely as Whites to be nonresponders at Wave 2, and African Americans were 23 percent as likely as Whites. Clearly, the effects of poverty duration is differentially associated with nonresponse for these three ethnocultural groups. Such a strong selection process has considerable implications for the potential bias in parameter estimates and confidence intervals, because it suggests that those who remain in the study over time are clearly and identifiably different from those who drop out. Additionally, that these findings replicated completely when the poor non-Hispanic White oversample was excluded suggests that these results are not artefactual. </p> <p>The effects of transitions into poverty were somewhat different. Whites who had experienced the sample average proportion of transitions were only two-thirds as likely to be nonresponders at Time 2 than those who had not experienced any transitions (again, this is most likely due to the strong negative consequences of long-term poverty). Hispanics with similar experiences of poverty transitions were 67 percent more likely than Whites to be Time 2 nonresponders, and African Americans 33 percent more likely. Thus, past poverty duration and transitions act in opposing directions for minority and nonminority members. </p> <p>Finally, we consider predictors of nonresponse at Times 3 and 4. Divorce was once again associated with an 82 percent greater probability (b = 0.60) of nonresponse, and being never-married with an 86 percent greater probability (b = 0.62). There was also an interaction between being Hispanic and past duration of poverty (b = 1.73). Relative to Whites, poverty duration was more strongly associated with nonresponse among Hispanics. </p> <p>In sum, we find substantial evidence that nonresponse at each wave is selective and related to demographic characteristics, family pathways, lifetime poverty experiences, and children's psychosocial adjustment. These findings suggest the possibility of considerable bias if corrections for selective nonresponse are not included in the analyses and also provide some insights into the mechanisms of missingness at work in our data and support for the idea that our data are at least partially MAR. </p> <hd id="AN0005530494-14"> C. Comparison of Results Using Listwise Deletion and Multiple Imputation </hd> <p>Below, we compare the results of listwise deletion and multiple imputation separately for Anxious/Depressed, and for Antisocial behavior. Because previous research suggests differences in antisocial behavior and anxiety-depression between boys and girls (for example, Cairns et al. 1988; Angold and Rutter 1992), these models were estimated using a multiple group comparison strategy that distinguished between these subgroups. Given the potentially large number of predictors, an initial model that included the additive and interactive effects of the poverty and race variables was estimated for boys and girls simultaneously. These models were trimmed (any variable significant in either equation was retained) and reestimated with control variables typically included in studies of poverty and children's well-being (mother's age at the child's birth, the mother's education, and whether the mother was never married or ever divorced). Listwise results did not indicate significant gender interactions for either outcome, and so results for boys and girls are combined for those analyses. </p> <hd id="AN0005530494-15"> D. Model Fit </hd> <p>Procedures for assessing model fit have not yet been implemented under multiple imputation. Imputation variance serves to increase the "noise" in assessing the fit of a specific model, and use of the full sample size also serves to inflate the model chi-square statistic (and also that of the independence model used for calculating fit indices such as the Normed Fit Index). Nevertheless, we present a range of information regarding the fit of our models as a rough guide for interpretation. Using listwise deletion, the selected model fit indices for antisocial behavior were: chi<sups>2</sups>(<reflink idref="bib80" id="ref6">80</reflink>) = 92.1, p = .17, RMSEA = .01, GFI = .98, NFI = .97. Median fit indices for multiple imputation results for antisocial behavior (minimum and maximum values in parentheses) were: chi<sups>2</sups>(<reflink idref="bib59" id="ref7">59</reflink>) = 125.3 (108.6-154.4), RMSEA = .037 (.032-.044), GFI = .99 (.99-.99), NFI = .99 (.99-.99). Fit indices for listwise results for anxious/depressed behavior were: chi<sups>2</sups>(<reflink idref="bib84" id="ref8">84</reflink>) = 127.3, p < .01, RMSEA = .03, GFI = .98, NFI = .95. Median fit indices for multiple imputation results for anxious/depressed behavior (minimum and maximum values in parentheses) were: chi<sups>2</sups>(<reflink idref="bib55" id="ref9">55</reflink>) = 105.6 (89.0-134.6), RMSEA = .033 (.030-.042), GFI = .99 (.99-.99), NFI = .99 (.99-1.00). By a variety of indicators, then, each model appears to provide an acceptable fit to the data, and so we proceed to interpret and contrast them below. </p> <hd id="AN0005530494-16"> E. Antisocial Behavior </hd> <p>Comparison of the results based on listwise deletion (LW) in Table 3 with those based on multiple imputation (MI) in Table 4 show several important similarities as well as some striking contrasts. One of the biggest differences is that an interaction between child sex and predictors of growth parameters emerges in the MI analyses that was not found when LW deletion was used. A similarity that is clear from examining both tables is that greater past duration of poverty is associated with higher initial levels of antisocial behavior for both boys and girls. Further, a finding that is not significant in the LW results is that contemporaneous poverty experiences are also important for predicting rates of increase in boys' antisocial behavior. Results for girls are also marginally significant. </p> <p>Another striking difference is also evident in comparing LW and MI results. Specifically, the presence of a negative coefficient for the interaction between African American status and past poverty duration suggests that poverty is less deleterious for African Americans than Whites. In fact, this finding suggests that, for African Americans, the longer the duration of poverty, the greater the rate of decrease in antisocial behavior. This disturbing finding disappears when the data are analyzed using multiple imputation to correct for selective nonresponse. Instead, an interaction, in the expected direction, emerges between Hispanic status and past transitions into poverty, suggesting that poverty transitions may be particularly injurious for initial levels of antisocial behavior among Hispanic boys. Finally, we also observe differences in the importance of mothers' marital history between LW and MI results. In the MI analyses, higher initial levels of antisocial behavior are observed among children whose mothers are never married. In contrast, the effects of mothers ever being divorced, associated with selective nonresponse, is no longer significant when moving from the LW results to the MI results. </p> <hd id="AN0005530494-17"> F. Anxious/Depressed Behavior </hd> <p>As with Antisocial behavior, a significant interaction between child sex and predictors of growth, not present in the LW results (Table 5) emerges when the MI results are considered (Table 6), perhaps because of the increased statistical power from analyses based on information from partial cases. Similarly, we find clear evidence of the importance of past poverty duration in predicting initial levels of anxiety/depression for both boys and girls. Additionally, in the MI but not LW results, being African American is associated with lower initial levels of anxiety/ depression for girls, and a slower rate of increase in anxiety/depression for boys. However, the interaction between African American status and past poverty duration is no longer significant in the MI results. In contrast, the negative association between i Hispanic status and initial levels of anxiety/depression found with the LW results disappears when the MI results are considered. An interaction between Hispanic status and past duration of poverty emerges, however, associated with greater rates of increase in anxious/depressed among Hispanics to Whites, again suggesting that more acute poverty experiences may be more deleterious for Hispanics than Whites.[<reflink idref="bib4" id="ref10">4</reflink>] A final difference between the two sets of analyses is that mother's age at child's birth, associated with selective nonresponse and present when LW deletion is used, is no longer significant in the MI analyses. Clearly, there is substantial evidence for differences between the results of analysis of the LW deleted data and MI, consistent with the idea that multiple imputation has corrected for selective nonresponse, providing less biased parameter estimates and standard errors. </p> <hd id="AN0005530494-18"> IV. Discussion </hd> <p>Previous research on selective attrition has tended to focus on issues such as the continued representativeness of a sample over time and have tended to conclude that bias due to nonrandom dropout are relatively small (for example, Burkham and Lee 1998; Fitzgerald, Gottschalk, and Moffitt 1998; MaCurdy, Mroz, and Gritz 1998; Ziliak and Kniesner 1998, and others in the same issue of the Journal of Human Resources). Most of these studies have focused on cross-sectional questions, however, rather than questions which involve inferences about variables which are derived from multiple time-points simultaneously. Clearly, predicting a status at a given point in time differs in fundamentally important ways from prediction of an individual's trajectory, particularly where selective nonresponse processes are likely to affect who remains in a data set over time. In this paper, we examined patterns and predictors of missing data in the NLSY, along with the potential bias introduced when addressing questions about development. Results were compared between the standard method of listwise deletion and multiple imputation, one of the most promising new methods for dealing with nonrandom study dropout, using data from the children of the NLSY participants. By creating multiple complete data sets, analyzing each separately, and then combining the results to form a single inference, results were obtained which corrected for the effects of selective attrition. Whereas listwise deletion of cases with missing data can lead to biased parameter estimates and incorrect standard errors, multiple imputation can correct for both of these shortcomings under the assumption that data are at least MAR. </p> <p>We found four clearly interpretable patterns of missing data in this study, each with its own set of predictors, indicating selective nonresponse in the NLSY. This is an issue that is particularly acute in longitudinal data sets and, as demonstrated, may affect the substantive conclusions reached. In this paper, application of multiple imputation to correct for selective nonresponse has substantially increased the validity and generalizability of these findings within the context of questions about time-dependent processes. </p> <p>Whereas some previous research suggests the effects of attrition in national longitudinal data sets may generally be small, this is not always the case, as the current study demonstrates. This is likely to be a particularly important consideration when complex longitudinal variables serve as the outcomes of interest, as with growth curve models and other similar dynamic models. </p> <p>Several potential extensions and needs are suggested by the present research, both substantively and methodologically. First, a greater variety of techniques for addressing issues of incomplete data in longitudinal data are required. A new software package, PAN (for PANel data) specifically designed for use with clustered sampling and longitudinal data sets has recently been reported in the literature (Schafer 1997, 2001), with a standalone version to be released shortly. This package takes full advantage of the known design characteristics to perform more efficient imputations, and is particularly useful for the situation where time-varying predictors of change are partially unobserved. Second, better strategies are needed for assessment of model fit with incomplete data in the context of structural equation models. These areas of inquiry have the potential to help us enrich our understanding of social processes at the same time that they extend applications of multiple imputation techniques. Finally, we hope to see more general application of multiple imputation strategies to longitudinal nationally representative data resources, perhaps even with the imputation done at the point of distribution where a highly general multiple imputation model would permit analysis of the resulting data sets by a very wide range of researchers, working from a common point of departure. Social scientists would benefit from greater training in the theory and application of multiple imputation techniques to correct for the effects of selective attrition in longitudinal research. </p> <p>Data from this article can be obtained from the authors from October 2002 through September 2005. [Submitted March 1999; accepted October 2000] </p> <p>1. Although not reported here, we also replicated these findings based on Full Information Maximum Likelihood, with virtually identical results. </p> <ulist> <item>2. Readers are likely curious about the inclusion of the poor non-Hispanic White oversample in our longitudinal analyses because data were not collected from them beyond 1990. Whenever the mechanism of missing data is known to the researcher, as it is in this case, no bias is introduced into the results because this process is precisely the requirement for data to be MAR in the classical sense (compare with Graham et al. 2001, on data which are "missing by design"). In any event, we reestimated our models excluding the oversample to examine the sensitivity of our results. Substantive findings replicate almost exactly when this oversample is excluded, suggesting that our results are not due to the inclusion of the oversample. All that changes as a result of inclusion/exclusion of the poor White oversample are estimates of nonresponse rates (52 percent nonresponse versus 43 percent nonresponse on at least one study variable). </item> <item>3. Repeated draws were made from </item> <ct id="AN0005530494-19"> p<subs>1</subs> (Y<subs>mis</subs>|Y<obs, X) = Integralf<subs>1</subs> (Y[sub mis] Y<subs>obs</subs>, X,q)p(q|Y<subs>obs</subs>, X)dq</ct> </ulist> <p>using a standard noninformative prior. </p> <p>4. This finding makes substantially greater sense than the Black X Current Poverty duration interaction found with listwise deleted results because, for all ethnocultural groups the effects of poverty are in the same direction (that is, greater duration of poverty associated with higher rates of increase in anxious/ depressed behavior), but are most pronounced for Hispanics. </p> <hd id="AN0005530494-20"> Table 1 </hd> <p>Sample Characteristics (N = 1,651) </p> <ct id="AN0005530494-21"> Variable Mean (SD) Child sex Boys 0.51 Girls 0.49 Race African American 0.32 Hispanic 0.21 Non-Hispanic White 0.47 Mother's age at child's birth 20.2 (2.2) Mother's years of education 11.3 (2.0) Mother ever divorced 0.30 Mother never married 0.18 Past duration of poverty (percent) 0.38 (0.37) Past transitions into poverty (percent) 0.11 (0.14) Current duration of poverty (percent) 0.30 (0.36) Current transitions into poverty (percent) 0.18 (0.38)</ct> <hd id="AN0005530494-22"> Table 2 </hd> <p>Logistic Regression Coefficients Predicting Patterns of Missing Data </p> <ct id="AN0005530494-23"> Legend for Chart: A - Predictor B - Missingness Pattern: Time I C - Missingness Pattern: Time 2 D - Missingness Pattern: Time Time 3 or 4 A B C D Child female 0.20 -0.40[a] -0.17 Past duration -0.14 1.51[c] -0.94 Past transitions 0.35 -3.74[a] 1.15 Mother ever divorced -0.00 0.81[d] 0.60[b] Mother never married -0.01 0.08 0.62[a] Anxiety/depression T1 -- 0.22[a] 0.08 Anxiety/depression T2 -- -- -0.12 Dependent T1 -- -0.04 -0.00 Dependent T2 -- -- -0.03 Hyperactive T1 -- -0.11 -0.03 Hyperactive T2 -- -- 0.04 Antisocial T1 -- -0.06 0.15 Antisocial T2 -- -- 0.10 Headstrong T1 -- -0.18[b] -0.07 Headstrong T2 -- -- -0.03 Hispanic -0.00 0.07 -0.10 African American 0.09 0.13 0.09 Mother's age at birth of child 0.16[d] 0.14[a] 0.01 Mother's education -0.01 -0.08 -0.06 Hispanic X past duration 0.55 -1.05 1.73[a] African American X past duration 0.01 -1.59[b] 1.42 Hispanic X past transitions -0.23 7.77[b] -1.44 African American X past transitions 0.22 5.16[b] -0.81 Valid N 1,232 980 879 df 13 18 23 chi<sups>2</sups> 26.1[a] 103.9[d] 49.2[b]</ct> <p>a p < .05 </p> <p>b p < .01 </p> <p>c p < .001 </p> <p>d p < .0001 </p> <hd id="AN0005530494-24"> Table 3 </hd> <p>Listwise Deletion Results Predicting Antisocial Behavior </p> <ct id="AN0005530494-25"> Legend for Chart: A - Variable B - Listwise Deletion Results (Boys = 401; Girls = 391): Level Estimate (SE) t-value C - Listwise Deletion Results (Boys = 401; Girls = 391): Shape Estimate (SE) t-value A B C Past duration 0.38 (0.13) 0.00 (0.07) 2.81 0.06 Past transitions -- -- Current duration -- 0.10 (0.07) -- 1.47 Current transitions -- -- Hispanic 0.15 (0.10) -0.09 (0.05) 1.43 -1.68 Black -0.10 (0.10) 0.08 (0.05) -1.03 1.65 Black X past duration -- -- Black X past transitions -- -- Black X current duration -- -0.34 (0.11) -- -2.94 Black X current transitions -- -- Hispanic X past duration -- -- Hispanic X past transitions -- -- Hispanic X current duration -- -0.14 (0.13) -- -1.05 Hispanic X current transitions -- -- Mother's education 0.01 (0.20) -0.02 (0.01) 0.23 -1.70 Mother's age at child's birth 0.02 (0.02) -0.01 (0.01) 0.79 -0.97 Mother never married 0.17 (0.13) -0.00 (0.06) 1.32 -0.04 Mother ever divorced -0.10 (0.09) 0.12 (0.05) -1.13 2.52</ct> <hd id="AN0005530494-26"> Table 4 </hd> <p>Multiple Imputation Results Predicting Antisocial Behavior </p> <ct id="AN0005530494-27"> Legend for Chart: A - Variable B - Boys (n = 848): Level Estimate (SE) t-value C - Boys (n = 848): Shape Estimate (SE) t-value D - Girls (n = 803): Level Estimate (SE) t-value E - Girls (n = 803): Shape Estimate (SE) t-value A B C D E Past duration 0.44(0.16) -0.00(0.10) 0.42(0.15) -0.06(0.09) 2.81 -0.02 2.84 -0.70 Past transitions 0.31(0.31) 0.01(0.16) 0.44(0.33) -0.09(0.17) 0.98 0.08 1.32 -0.56 Current duration -- 0.15(0.07) -- 0.15(0.08) -- 1.98 -- 1.91 Current transition -- -- -- -- Black -0.19(0.11) 0.04(0.06) 0.04(0.11) 0.02(0.06) -1.77 0.64 0.37 0.28 Hispanic -0.04(0.11) -0.05(0.06) 0.10(0.12) -0.09(0.06) -0.35 -0.82 0.79 -1.45 Black x past duration -- -- -- -- Black x past transitions -- -- -- -- Black x current duration -- -- -- -- Black x current transitions -- -- -- -- Hispanic x past duration -- -- -- -- Hispanic x past transitions 1.55(0.70) -0.36(0.34) 0.09(0.75) -0.26(0.39) 2.21 -1.06 0.13 -0.66 Hispanic x current duration -- -- -- -- Hispanic x current transitions -- -- -- -- Mother's education -0.03(0.02) 0.00(0.01) 0.01(0.03) -0.02(0.01) -1.14 0.34 0.35 -1.09 Mother's age at child's birth -0.01(0.02) -0.01(0.01) 0.03(0.02) -0.01(0.01) -0.05 -1.16 1.74 -1.22 Mother never married 0.35(0.16) -0.05(0.08) -0.02(0.14) -0.00(0.09) 2.21 -0.59 -0.17 -0.02 Mother ever divorced 0.01(0.11) 0.04(0.05) -0.09(0.11) 0.13(0.07) 0.12 0.74 -0.79 1.87</ct> <hd id="AN0005530494-28"> Table 5 </hd> <p>Listwise Deletion Results Predicting Anxious/Depressed Behavior </p> <ct id="AN0005530494-29"> Legend for Chart: A - Variable B - Listwise Deletion Results (Boys = 401; Girls = 391): Level Estimate (SE) t-value C - Listwise Deletion Results (Boys = 401; Girls = 391):Shape Estimate (SE) t-value A B C Past duration 0.50(0.12) -0.07(0.07) 4.17 -0.94 Past transitions -0.18(0.27) 0.25(0.14) -0.66 1.76 Current duration -- -0.01(0.06) -0.21 Current transitions -- -- Hispanic -0.27(0.09) -0.05(0.05) -3.03 -1.02 Black -0.01(0.09) -0.03(0.05) -0.05 -0.55 Black X past duration -0.18(0.25) 0.31(0.13) -0.74 2.33 Black X past transitions -0.05(0.61) 0.34(0.33) -0.09 1.02 Black X current duration -- -- Black X current transitions -- -- Hispanic X past duration -- -- Hispanic x past transitions -- -- Hispanic x current duration -- -- Hispanic x current transitions -- -- Mother's education 0.01(0.02) -0.01(0.01) 0.34 -1.25 Mother's age at child's birth -0.02(0.02) 0.02(0.01) -1.04 2.74 Mother never married -0.12(0.11) 0.06(0.06) -1.10 0.99 Mother ever divorced -0.00(0.08) 0.07(0.04) -0.04 1.55</ct> <hd id="AN0005530494-30"> Table 6 </hd> <p>Multiple Imputation Results Predicting Anxious/Depressed Behavior </p> <ct id="AN0005530494-31"> Legend for Chart: A - A - Variable B - B - Boys (n = 848):Level Estimate (SE) t-value C - C - Boys (n = 848):Level Estimate (SE) t-value D - Girls (n = 803):Shape Estimate (SE) t-value E - Girls (n = 803):Shape Estimate (SE) t-value A B C D E Past duration .035(0.12) -0.02(0.07) 0.40(0.11) 0.01(0.07) 2.97 -0.23 3.44 0.17 Past transitions -0.16(0.25) 0.26(0.14) -0.13(0.29) 0.18(0.15) -0.64 1.81 -0.46 1.17 Current duration -- -- -- -- Current transitions -- -- -- -- Black -0.04(0.09) -0.21(0.06) -0.31(0.09) 0.01(0.05) -0.40 -3.66 -3.29 0.17 Hispanic -0.05(0.10) 0.08(0.05) -0.00(0.10) -0.04(0.06) -0.48 -1.57 -0.10 -0.69 Black x past duration -- -- -- -- Black x past transitions -- -- -- -- Black x current duration -- -- -- -- Black x current transitions -- -- -- -- Hispanic x past duration -0.18(0.23) 0.31(0.13) -0.17(0.27) 0.18(0.15) -0.79 2.38 -0.64 1.18 Hispanic x past transitions -- -- -- -- Hispanic x current duration -- -- -- -- Hispanic x current transitions -- -- -- -- Mother's education -0.00(0.02) -0.00(0.01) 0.02(0.02) -0.02(0.01) -0.25a -0.22 1.03 -1.28 Mother's age at child's birth -0.02(0.02) 0.01(0.01) -0.03(0.02) 0.02(0.01) -0.86 0.80 -1.47 1.57 Mother never married -0.02(0.12) 0.07(0.07) -0.05(0.11) -0.09(0.07) -0.18 1.02 -0.45 -1.29 Mother ever divorced 0.07(0.09) 0.05(0.05) 0.01(0.09) 0.06(0.06) 0.78 0.81 0.15 1.09</ct> <hd id="AN0005530494-32"> References </hd> <p>Allison, P. D. 1987. "Estimation of Linear Models with Incomplete Data." In Sociological Methodology, ed. C. C. Clogg, 71-103. Washington, D.C.: American Sociological Association. </p> <p>Anderson, T. W. 1957. "Maximum Likelihood Estimation for the Multivariate Normal Distribution When Some Observations Are Missing." Journal of the American Statistical Association 52:200-203. </p> <p>Arbuckle, J. L. 1995. Amos for Windows. Analysis of Moment Structures, Version 3.5. Chicago: Small Waters Corp. </p> <p>-- -- . 1996. "Full Information Estimation in the Presence of Incomplete Data." In Advanced Structural Equation Modeling: Issues and techniques, ed. G. A. Marcoulides and R. E. Schumacker, 243-77. Mahwah, N.J.: Erlbaum. </p> <p>Dempster, A. P., Laird, N. M., and Rubin, D. B. 1977. Maximum Likelihood from Incomplete Data via the Em Algorithm. Journal of the Royal Statistical Society B(<reflink idref="bib39" id="ref11">39</reflink>):1-38. Ezzati-Rice, T. M., Johnson, W., Khare, M., Little, R. J. A., Rubin, D. B., and Schafer, J. </p> <p>L. 1995. "A Simulation Study to Evaluate the Performance Little, R. J., and Rubin, D. B. 1987. Statistical Analysis with Missing Data. New York: John Wiley and Sons. </p> <p>-- -- . 1989. "The Analysis of Social Science Data with Missing Values." Sociological Methods and Research 18:292-326. </p> <p>Meng, X. L., and Rubin, D. B. 1992. "Performing Likelihood Ratio Tests with Multiply-imputed Data Sets." Biometrika 79:103-11. </p> <p>Rubin, D. B. 1987. Multiple Imputation for Nonresponse in Surveys. New York: John Wiley and Sons. </p> <p>Shafer, J. L. (2001). "Multiple Imputation with PAN." In New Methods for the Analysis of Change, ed. L. M. Collins and A. G. Sayer, 355-77. Washington, D.C.: American Psychological Association. </p> <p>-- -- . 1997. Analysis of Incomplete Multivariate Data. London: Chapman and Hall. </p> <p>Schafer, J. L., and Olsen, M. K. 1998. "Multiple Imputation for Multivariate Missing-data Problems: a Data Analyst's Perspective." Multivariate Behavioral Research 33:545-71. </p> <p>Shanahan, M. J., Davey, A., and Brooks, J. 1998. "Dynamic Patterns of Poverty and Psychosocial Adjustment Through Childhood." Unpublished. </p> <p>Willett, J. B., and Sayer, A. G. 1994. "Using Covariance Structure Analysis to Detect Correlates and Predictors of Individual Change over Time." Psychological Bulletin 116: 363-81. </p> <p>-- -- . 1996. "Cross-domain Analyses of Change over Time: Combining Growth Modeling and Covariance Structure Analysis." In Advanced Structural Equation Modeling: Issues and Techniques, ed. G. A. Marcoulides and R. E. Schumacker, 125-57. Mahwah, N.J.: Lawrence Erlbaum Associates. </p> <aug> <p>By Adam Davey; Michael J. Shanahan and Joseph L. Schafer </p> <p></p> <p>Adam Davey is a professor of child and family development at the University of Georgia </p> <p>Michael J. Shanahan is an associate professor of human development and an adjunct professor of sociology at the Pennsylvania State University, as well as a research affiliate at the Population Research Institute </p> <p>Joseph L. Schafer is an associate professor of statistics at the Pennsylvania State University. </p> </aug> <nolink nlid="nl1" bibid="bib1" firstref="ref1"></nolink> <nolink nlid="nl2" bibid="bib2" firstref="ref2"></nolink> <nolink nlid="nl3" bibid="bib3" firstref="ref3"></nolink> <nolink nlid="nl4" bibid="bib80" firstref="ref6"></nolink> <nolink nlid="nl5" bibid="bib59" firstref="ref7"></nolink> <nolink nlid="nl6" bibid="bib84" firstref="ref8"></nolink> <nolink nlid="nl7" bibid="bib55" firstref="ref9"></nolink> <nolink nlid="nl8" bibid="bib4" firstref="ref10"></nolink> <nolink nlid="nl9" bibid="bib39" firstref="ref11"></nolink>
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  Data: Correcting for Selective Nonresponse in the National Longitudinal Survey of Youth Using Multiple Imputation.
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  Data: Principal components analysis revealed four patterns of nonresponse on children's psychosocial adjustment, lifetime poverty experiences, and family history. Results from examining latent growth curve models using listwise deletion and multiple imputation indicated that multiple imputation corrected for selective nonresponse, providing less-biased estimates and standard errors. (Contains 18 references.) (SK)
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