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1.
When missingness is suspected to be not at random (MNAR) in longitudinal studies, researchers sometimes compare the fit of a target model that assumes missingness at random (here termed a MAR model) and a model that accommodates a hypothesized MNAR missingness mechanism (here termed a MNAR model). It is well known that such comparisons are only interpretable conditional on the validity of the chosen MNAR model’s assumptions about the missingness mechanism. For that reason, researchers often perform a sensitivity analysis comparing the MAR model to not one, but several, plausible alternative MNAR models. In the social sciences, it is not widely known that such model comparisons can be particularly sensitive to case influence, such that conclusions drawn could depend on a single case. This article describes two convenient diagnostics suited for detecting case influence on MAR–MNAR model comparisons. Both diagnostics require much less computational burden than global influence diagnostics that have been used in other disciplines for MNAR sensitivity analyses. We illustrate the interpretation and implementation of these diagnostics with simulated and empirical latent growth modeling examples. It is hoped that this article increases awareness of the potential for case influence on MAR–MNAR model comparisons and how it could be detected in longitudinal social science applications.  相似文献   

2.
The purpose of this study is to investigate the effects of missing data techniques in longitudinal studies under diverse conditions. A Monte Carlo simulation examined the performance of 3 missing data methods in latent growth modeling: listwise deletion (LD), maximum likelihood estimation using the expectation and maximization algorithm with a nonnormality correction (robust ML), and the pairwise asymptotically distribution-free method (pairwise ADF). The effects of 3 independent variables (sample size, missing data mechanism, and distribution shape) were investigated on convergence rate, parameter and standard error estimation, and model fit. The results favored robust ML over LD and pairwise ADF in almost all respects. The exceptions included convergence rates under the most severe nonnormality in the missing not at random (MNAR) condition and recovery of standard error estimates across sample sizes. The results also indicate that nonnormality, small sample size, MNAR, and multicollinearity might adversely affect convergence rate and the validity of statistical inferences concerning parameter estimates and model fit statistics.  相似文献   

3.
Competence data from low‐stakes educational large‐scale assessment studies allow for evaluating relationships between competencies and other variables. The impact of item‐level nonresponse has not been investigated with regard to statistics that determine the size of these relationships (e.g., correlations, regression coefficients). Classical approaches such as ignoring missing values or treating them as incorrect are currently applied in many large‐scale studies, while recent model‐based approaches that can account for nonignorable nonresponse have been developed. Estimates of item and person parameters have been demonstrated to be biased for classical approaches when missing data are missing not at random (MNAR). In our study, we focus on parameter estimates of the structural model (i.e., the true regression coefficient when regressing competence on an explanatory variable), simulating data according to various missing data mechanisms. We found that model‐based approaches and ignoring missing values performed well in retrieving regression coefficients even when we induced missing data that were MNAR. Treating missing values as incorrect responses can lead to substantial bias. We demonstrate the validity of our approach empirically and discuss the relevance of our results.  相似文献   

4.
This article is concerned with the question of whether the missing data mechanism routinely referred to as missing completely at random (MCAR) is statistically examinable via a test for lack of distributional differences between groups with observed and missing data, and related consequences. A discussion is initially provided, from a formal logic standpoint, of the distinction between necessary conditions and sufficient conditions. This distinction is used to argue then that testing for lack of these group distributional differences is not a test for MCAR, and an example is given. The view is next presented that the desirability of MCAR has been frequently overrated in empirical research. The article is finalized with a reference to principled, likelihood-based methods for analyzing incomplete data sets in social and behavioral research.  相似文献   

5.
A well-known ad-hoc approach to conducting structural equation modeling with missing data is to obtain a saturated maximum likelihood (ML) estimate of the population covariance matrix and then to use this estimate in the complete data ML fitting function to obtain parameter estimates. This 2-stage (TS) approach is appealing because it minimizes a familiar function while being only marginally less efficient than the full information ML (FIML) approach. Additional advantages of the TS approach include that it allows for easy incorporation of auxiliary variables and that it is more stable in smaller samples. The main disadvantage is that the standard errors and test statistics provided by the complete data routine will not be correct. Empirical approaches to finding the right corrections for the TS approach have failed to provide unequivocal solutions. In this article, correct standard errors and test statistics for the TS approach with missing completely at random and missing at random normally distributed data are developed and studied. The new TS approach performs well in all conditions, is only marginally less efficient than the FIML approach (and is sometimes more efficient), and has good coverage. Additionally, the residual-based TS statistic outperforms the FIML test statistic in smaller samples. The TS method is thus a viable alternative to FIML, especially in small samples, and its further study is encouraged.  相似文献   

6.
Latent class models are often used to assign values to categorical variables that cannot be measured directly. This “imputed” latent variable is then used in further analyses with auxiliary variables. The relationship between the imputed latent variable and auxiliary variables can only be correctly estimated if these auxiliary variables are included in the latent class model. Otherwise, point estimates will be biased. We develop a method that correctly estimates the relationship between an imputed latent variable and external auxiliary variables, by updating the latent variable imputations to be conditional on the external auxiliary variables using a combination of multiple imputation of latent classes and the so-called three-step approach. In contrast with existing “one-step” and “three-step” approaches, our method allows the resulting imputations to be analyzed using the familiar methods favored by substantive researchers.  相似文献   

7.
The inclusion of covariates improves the prediction of class memberships in latent class analysis (LCA). Several methods for examining covariate effects have been developed over the past decade; however, researchers have limited to the comparisons of the performance among these methods in cases of the single-level LCA. The present study investigated the performance of three different methods for examining covariate effects in a multilevel setting. We conducted a simulation to compare the performance of the three methods when level-1 and level-2 covariates were simultaneously incorporated into the nonparametric multilevel latent class model to predict latent class membership at each level. The simulation results revealed that the bias-adjusted three-step maximum likelihood method performed equally well as the one-step method when the sample sizes were sufficiently large and the latent classes were distinct from each other. However, the unadjusted three-step method significantly underestimated the level-1 covariate effect in most conditions.

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8.
Latent class (LC) analysis is widely used in the social and behavioral sciences to find meaningful clusters based on a set of categorical variables. To deal with the common problem that a standard LC analysis may yield a large number classes and thus a solution that is difficult to interpret, recently an alternative approach has been proposed, called Latent Class Tree (LCT) analysis. It involves starting with a solution with a small number of “basic” classes, which may subsequently be split into subclasses at the next stages of an analysis. However, in most LC analysis applications, we not only wish to identify the relevant classes, but also want to see how they relate to external variables (covariates or distal outcomes). For this purpose, researchers nowadays prefer using the bias-adjusted three-step method. Here, we show how this bias-adjusted three-step procedure can be applied in the context of LCT modeling. More specifically, an R-package is presented that performs a three-step LCT analysis: it builds a LCT and allows checking how splits are related to the relevant external variables. The new tool is illustrated using a cross-sectional application with multiple indicators on social capital and demographics as external variables and with a longitudinal application with a mood variable measured multiple times during the day and personality traits as external variables.  相似文献   

9.
A latent variable modeling approach to evaluate scale reliability under realistic conditions in empirical behavioral and social research is discussed. The method provides point and interval estimation of reliability of multicomponent measuring instruments when several assumptions are violated. These assumptions include missing data, correlated errors, nonnormality, lack of unidimensionality, and data not missing at random. The procedure can be readily used to aid scale construction and development efforts in applied settings, and is illustrated using data from an educational study.  相似文献   

10.
The purpose of this study is to develop and evaluate unidimensional models that can handle semiordered data within scale items (i.e., items with multiple ordered response categories, and one additional nominal response category). We apply the models to scale data with not applicable (NA) responses to compare the model performance to conditions in which NA responses are treated as missing and ignored. We also conduct a small simulation study based on the operational study to evaluate the parameter recovery of the models under the operational conditions. Findings indicate that the proposed models show promise for (a) reducing standard errors of trait estimates for persons who select NA responses, (b) reducing nonresponse bias in trait estimates for persons who select NA responses, and (c) providing substantive information to practitioners about the nature of the relationship between NA selection and the trait of measurement.  相似文献   

11.
Myriad approaches for handling missing data exist in the literature. However, few studies have investigated the tenability and utility of these approaches when used with intensive longitudinal data. In this study, we compare and illustrate two multiple imputation (MI) approaches for coping with missingness in fitting multivariate time-series models under different missing data mechanisms. They include a full MI approach, in which all dependent variables and covariates are imputed simultaneously, and a partial MI approach, in which missing covariates are imputed with MI, whereas missingness in the dependent variables is handled via full information maximum likelihood estimation. We found that under correctly specified models, partial MI produces the best overall estimation results. We discuss the strengths and limitations of the two MI approaches, and demonstrate their use with an empirical data set in which children’s influences on parental conflicts are modeled as covariates over the course of 15 days (Schermerhorn, Chow, & Cummings, 2010).  相似文献   

12.
Small samples are common in growth models due to financial and logistical difficulties of following people longitudinally. For similar reasons, longitudinal studies often contain missing data. Though full information maximum likelihood (FIML) is popular to accommodate missing data, the limited number of studies in this area have found that FIML tends to perform poorly with small-sample growth models. This report demonstrates that the fault lies not with how FIML accommodates missingness but rather with maximum likelihood estimation itself. We discuss how the less popular restricted likelihood form of FIML, along with small-sample-appropriate methods, yields trustworthy estimates for growth models with small samples and missing data. That is, previously reported small sample issues with FIML are attributable to finite sample bias of maximum likelihood estimation not direct likelihood. Estimation issues pertinent to joint multiple imputation and predictive mean matching are also included and discussed.  相似文献   

13.
A procedure for evaluating candidate auxiliary variable correlations with response variables in incomplete data sets is outlined. The method provides point and interval estimates of the outcome-residual correlations with potentially useful auxiliaries, and of the bivariate correlations of outcome(s) with the latter variables. Auxiliary variables found in this way can enhance considerably the plausibility of the popular missing at random (MAR) assumption if included in ensuing maximum likelihood analyses, or can alternatively be incorporated in imputation models for subsequent multiple imputation analyses. The approach can be particularly helpful in empirical settings where violations of the MAR assumption are suspected, as is the case in many longitudinal studies, and is illustrated with data from cognitive aging research.  相似文献   

14.
Latent class methods can be used to identify unobserved subgroups which differ in their observed data. Researchers are often interested in outcomes for the identified subgroups and in some disciplines time-to-event outcome measures are common, e.g., overall survival in oncology. In this study Monte Carlo simulation is used to evaluate the empirical properties of latent class effect estimates on a time-to-event distal outcome using one, two and three-step approaches. Both standard and inclusive bias-corrected three-step approaches are considered. One-step latent class effect estimates are shown to be superior to the evaluated alternatives. Both the two-step approach and a standard three-step approach, where subjects are partially assigned to latent classes, produced unbiased estimates with nominal confidence interval coverage when latent classes were well separated, but not otherwise.

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15.
Respondent attrition is a common problem in national longitudinal panel surveys. To make full use of the data, weights are provided to account for attrition. Weight adjustments are based on sampling design information and data from the base year; information from subsequent waves is typically not utilized. Alternative methods to address bias from nonresponse are full information maximum likelihood (FIML) or multiple imputation (MI). The effects on bias of growth parameter estimates from using these methods are compared via a simulation study. The results indicate that caution needs to be taken when utilizing panel weights when there is missing data, and to consider methods like FIML and MI, which are not as susceptible to the omission of important auxiliary variables.  相似文献   

16.
The authors investigated 2 issues concerning the power of latent growth modeling (LGM) in detecting linear growth: the effect of the number of repeated measurements on LGM's power in detecting linear growth and the comparison between LGM and some other approaches in terms of power for detecting linear growth. A Monte Carlo simulation design was used, with 3 crossed factors (growth magnitude, number of repeated measurements, and sample size) and 1,000 replications within each cell condition. The major findings were as follows: For 3 repeated measurements, a substantial proportion of samples failed to converge in structural equation modeling; the number of repeated measurements did not show any effect on the statistical power of LGM in detecting linear growth; and the LGM approach outperformed both the dependent t test and repeated-measures analysis of variance (ANOVA) in terms of statistical power for detecting growth under the conditions of small growth magnitude and small to moderate sample size conditions. The multivariate repeated-measures ANOVA approach consistently underperformed the other tests.  相似文献   

17.
A multiple testing procedure for examining the assumption of normality that is often made in analyses of incomplete data sets is outlined. The method is concerned with testing normality within each missingness pattern and arriving at an overall statement about normality using the available data. The approach is readily applied in empirical research with missing data using the popular software Mplus, Stata, and R. The procedure can be used to ascertain a main assumption underlying frequent applications of maximum likelihood in incomplete data modeling with continuous outcomes. The discussed approach is illustrated with numerical examples.  相似文献   

18.
Emphasis on improving higher level biology education continues. A new two-step approach to the experimental phases within an outreach gene technology lab, derived from cognitive load theory, is presented. We compared our approach using a quasi-experimental design with the conventional one-step mode. The difference consisted of additional focused discussions combined with students writing down their ideas (step one) prior to starting any experimental procedure (step two). We monitored students’ activities during the experimental phases by continuously videotaping 20 work groups within each approach (N = 131). Subsequent classification of students’ activities yielded 10 categories (with well-fitting intra- and inter-observer scores with respect to reliability). Based on the students’ individual time budgets, we evaluated students’ roles during experimentation from their prevalent activities (by independently using two cluster analysis methods). Independently of the approach, two common clusters emerged, which we labeled as ‘all-rounders’ and as ‘passive students’, and two clusters specific to each approach: ‘observers’ as well as ‘high-experimenters’ were identified only within the one-step approach whereas under the two-step conditions ‘managers’ and ‘scribes’ were identified. Potential changes in group-leadership style during experimentation are discussed, and conclusions for optimizing science teaching are drawn.  相似文献   

19.
A 2-stage robust procedure as well as an R package, rsem, were recently developed for structural equation modeling with nonnormal missing data by Yuan and Zhang (2012). Several test statistics that have been used for complete data analysis are employed to evaluate model fit in the 2-stage robust method. However, properties of these statistics under robust procedures for incomplete nonnormal data analysis have never been studied. This study aims to systematically evaluate and compare 5 test statistics, including a test statistic derived from normal-distribution-based maximum likelihood, a rescaled chi-square statistic, an adjusted chi-square statistic, a corrected residual-based asymptotical distribution-free chi-square statistic, and a residual-based F statistic. These statistics are evaluated under a linear growth curve model by varying 8 factors: population distribution, missing data mechanism, missing data rate, sample size, number of measurement occasions, covariance between the latent intercept and slope, variance of measurement errors, and downweighting rate of the 2-stage robust method. The performance of the test statistics varies and the one derived from the 2-stage normal-distribution-based maximum likelihood performs much worse than the other four. Application of the 2-stage robust method and of the test statistics is illustrated through growth curve analysis of mathematical ability development, using data on the Peabody Individual Achievement Test mathematics assessment from the National Longitudinal Survey of Youth 1997 Cohort.  相似文献   

20.
The purpose of this study was to describe the reflections of adults with visual impairments regarding bullying experiences during their school-based education. An interpretative phenomenological analysis research approach was used and 11 participants (aged 20–35 years; seven women, four men) participated in this study. The sources of data were semi-structured audiotaped telephone interviews and reflective field notes. Thematic development was undertaken utilizing a three-step analytical process guided by the research approach. Based on the data analysis, three interrelated themes were constructed: (a) “It would be when they knew there weren't teachers watching”: bullying experiences in unowned and unstructured spaces; (b) “Going through the motions”: feelings about verbal, social, and physical victimization; and (c) “They had their own insecurities”: understanding the bullies and bystanders. The emerged themes provide a unique insight into the way in which those with visual impairments experienced bullying in schools and the meaning they ascribed to those experiences.  相似文献   

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