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1.
Application of Latent Growth Curve Analysis With Categorical Responses in Social Behavioral Research
Tae Kyoung Lee Kandauda Wickrama Catherine W. O’Neal 《Structural equation modeling》2018,25(2):294-306
Latent growth modeling allows social behavioral researchers to investigate within-person change and between-person differences in within-person change. Typically, conventional latent growth curve models are applied to continuous variables, where the residuals are assumed to be normally distributed, whereas categorical variables (i.e., binary and ordinal variables), which do not hold to normal distribution assumptions, have rarely been used. This article describes the latent growth curve model with categorical variables, and illustrates applications using Mplus software that are applicable to social behavioral research. The illustrations use marital instability data from the Iowa Youth and Family Project. We close with recommendations for the specification and parameterization of growth models that use both logit and probit link functions. 相似文献
2.
W. Holmes Finch Jerrell C. Cassady 《Educational Assessment, Evaluation and Accountability》2014,26(2):177-201
In the USA, trends in educational accountability have driven several models attempting to provide quality data for decision making at the national, state, and local levels, regarding the success of schools in meeting standards for competence. Statistical methods to generate data for such decisions have generally included (a) status models that examine simple indications of number of students meeting a criterion level of achievement, (b) growth models that explore change over the course of one or more years, and (c) value-added models that attempt to control for factors deemed relevant to student achievement patterns. This study examined a new strategy for student and school achievement modeling that augments the field through the use of the probit model to estimate the likelihood of students meeting an established level standard and estimating the proportion of individuals within a school meeting the standard. Results of the study showed that the probit model was an effective tool both for providing such adjustments, as well as for adjusting them based upon salient demographic variables. Implications of these results and suggestions for further use of the model are discussed. 相似文献
3.
Growth mixture models combine latent growth curve models and finite mixture models to examine the existence of latent classes that follow distinct developmental patterns. Analyses based on these models are becoming quite common in social and behavioral science research because of recent advances in computing, the availability of specialized statistical programs, and the ease of programming. In this article, we show how mixture models can be fit to examine the presence of multiple latent classes by algorithmically grouping or clustering individuals who follow the same estimated growth trajectory based on an evaluation of individual case residuals. The approach is illustrated using empirical longitudinal data along with an easy to use computerized implementation. 相似文献
4.
Mohammed Saqr 《British journal of educational technology : journal of the Council for Educational Technology》2023,54(5):1077-1094
Learning analytics is a fast-growing discipline. Institutions and countries alike are racing to harness the power of using data to support students, teachers and stakeholders. Research in the field has proven that predicting and supporting underachieving students is worthwhile. Nonetheless, challenges remain unresolved, for example, lack of generalizability, portability and failure to advance our understanding of students' behaviour. Recently, interest has grown in modelling individual or within-person behaviour, that is, understanding the person-specific changes. This study applies a novel method that combines within-person with between-person variance to better understand how changes unfolding at the individual level can explain students' final grades. By modelling the within-person variance, we directly model where the process takes place, that is the student. Our study finds that combining within- and between-person variance offers a better explanatory power and a better guidance of the variables that could be targeted for intervention at the personal and group levels. Furthermore, using within-person variance opens the door for person-specific idiographic models that work on individual student data and offer students support based on their own insights.
Practitioner notes
What is already known about this topic- Predicting students' performance has commonly been implemented using cross-sectional data at the group level.
- Predictive models help predict and explain student performance in individual courses but are hard to generalize.
- Heterogeneity has been a major factor in hindering cross-course or context generalization.
- Intra-individual (within-person) variations can be modelled using repeated measures data.
- Hybrid between–within-person models offer more explanatory and predictive power of students' performance.
- Intra-individual variations do not mirror interindividual variations, and thus, generalization is not warranted.
- Regularity is a robust predictor of student performance at both the individual and the group levels.
- The study offers a method for teachers to better understand and predict students' performance.
- The study offers a method of identifying what works on a group or personal level.
- Intervention at the personal level can be more effective when using within-person predictors and at the group level when using between-person predictors.
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6.
Elizabeth M. Planalp Han Du Julie M. Braungart-Rieker 《Structural equation modeling》2017,24(1):129-147
Although methodology articles have increasingly emphasized the need to analyze data from two members of a dyad simultaneously, the most popular method in substantive applications is to examine dyad members separately. This might be due to the underappreciation of the extra information simultaneous modeling strategies can provide. Therefore, the goal of this study was to compare multiple growth curve modeling approaches for longitudinal dyadic data (LDD) in both structural equation modeling and multilevel modeling frameworks. Models separately assessing change over time for distinguishable dyad members are compared to simultaneous models fitted to LDD from both dyad members. Furthermore, we compared the simultaneous default versus dependent approaches (whether dyad pairs’ Level 1 [or unique] residuals are allowed to covary and differ in variance). Results indicated that estimates of variance and covariance components led to conflicting results. We recommend the simultaneous dependent approach for inferring differences in change over time within a dyad. 相似文献
7.
Developmentalists are often interested in understanding change processes, and growth models are the most common analytic tool for examining such processes. Nonlinear growth curves are especially valuable to developmentalists because the defining characteristics of the growth process such as initial levels, rates of change during growth spurts, and asymptotic levels can be estimated. A variety of growth models are described beginning with the linear growth model and moving to nonlinear models of varying complexity. A detailed discussion of nonlinear models is provided, highlighting the added insights into complex developmental processes associated with their use. A collection of growth models are fit to repeated measures of height from participants of the Berkeley Growth and Guidance Studies from early childhood through adulthood. 相似文献
8.
Popular longitudinal models allow for prediction of growth trajectories in alternative ways. In latent class growth models (LCGMs), person-level covariates predict membership in discrete latent classes that each holistically define an entire trajectory of change (e.g., a high-stable class vs. late-onset class vs. moderate-desisting class). In random coefficient growth models (RCGMs, also known as latent curve models), however, person-level covariates separately predict continuously distributed latent growth factors (e.g., an intercept vs. slope factor). This article first explains how complex and nonlinear interactions between predictors and time are recovered in different ways via LCGM versus RCGM specifications. Then a simulation comparison illustrates that, aside from some modest efficiency differences, such predictor relationships can be recovered approximately equally well by either model—regardless of which model generated the data. Our results also provide an empirical rationale for integrating findings about prediction of individual change across LCGMs and RCGMs in practice. 相似文献
9.
Path analysis and residual plotting as methods of environmental scanning in higher education: An illustration with applications and enrollments 总被引：1，自引：0，他引：1
In this study we propose using path analysis and residual plotting as methods supporting environmental scanning in strategic planning for higher education institutions. As an illustration, path models of three levels of independent variables, that is, socioeconomic background, current economic variables, and educational variables, are developed. The dependent variables measuring applications and enrollments at a research university, Virginia Tech, and enrollments at four-year institutions in Virginia are regressed on the independent variables. The residuals from the multiple regression models are plotted on the county maps of Virginia to identify the geographic regions in which the applications and enrollments at Virginia Tech and the enrollments in colleges and universities of Virginia are higher or lower than expected according to the models. The implications of the variables in the models and the geographic distributions of residuals for strategic planning decisions are discussed. 相似文献
10.
This article shows that the mean and covariance structure of the predetermined autoregressive latent trajectory (ALT) model are very flexible. As a result, the shape of the modeled growth curve can be quite different from what one might expect at first glance. This is illustrated with several numerical examples that show that, for example, a linear trajectory might be present among the model predicted scores even though no latent change parameter was included in the model. In addition, 2 examples are given that show that the predetermined ALT model can fit to data generated by models with model structures that are rather different from that of the ALT model itself. The practical relevance of these findings is demonstrated using an empirical example. We end by providing recommendations for researchers considering the use of the predetermined ALT model. 相似文献
11.
Trang Quynh Nguyen Yenny Webb-Vargas Ina M. Koning Elizabeth A. Stuart 《Structural equation modeling》2016,23(3):368-383
We investigate a method to estimate the combined effect of multiple continuous/ordinal mediators on a binary outcome: (a) fit a structural equation model with probit link for the outcome and identity/probit link for continuous/ordinal mediators, (b) predict potential outcome probabilities, and (c) compute natural direct and indirect effects. Step 2 involves rescaling the latent continuous variable underlying the outcome to address residual mediator variance and covariance. We evaluate the estimation of risk-difference- and risk-ratio-based effects (RDs, RRs) using the maximum likelihood (ML), mean-and-variance-adjusted weighted least squares (WLSMV) and Bayes estimators in Mplus. Across most variations in path-coefficient and mediator-residual-correlation signs and strengths, and confounding situations investigated, the method performs well with all estimators, but favors ML/WLSMV for RDs with continuous mediators, and Bayes for RRs with ordinal mediators. Bayes outperforms ML/WLSMV regardless of mediator type when estimating RRs with small potential outcome probabilities and in two other special cases. An adolescent alcohol prevention study is used for illustration. 相似文献
12.
This study evaluates latent differential equation models on binary and ordinal data. Binary and ordinal data are widely used in psychology research and many statistical models have been developed, such as the probit model and the logit model. We combine the latent differential equation model with the probit model through a threshold approach, and then compare the threshold model with a naive model, which blindly treats binary and ordinal data as continuous. Simulation results suggest that the naive model leads to bias on binary data and on ordinal data with fewer than 5 levels, whereas the threshold model is unbiased and efficient for binary and ordinal data. Two example analyses on empirical binary data and ordinal data show that the threshold model also has better external validity. The R code for the threshold model is provided. 相似文献
13.
Lucia Mason 《Instructional Science》1994,22(3):157-187
This study is a qualitative investigation on the teaching-learning by analogy of complex curriculum concepts in natural and relevant environments, such as classrooms, to improve the ecological validity of the research itself. It aimed at exploring whether students' successful use of analogy in learning science was related a) to the level of their understanding of a specific analogy and b) to their metacognitive awareness of how the analogy was to be used and of the changes produced in their own conceptual structures. During the implementation of a biological curriculum unit, sixty 5th graders were engaged in understanding the ways in which the new concepts (concerning the human circulatory system) were similar to a familiar source (the mail delivery system) by detecting all the relations between the two systems and mapping the relevant information from the source to the target. Learners' preexisting mental models have been taken into account in order to examine their conceptual growth and change via the analogy. Qualitative data are presented for the analysis of elicited and spontaneous analogical inferences, based on structural and semantic similarities, as well as of the identification of where the analogy breaks down. Moreover, qualitative data also concern children's metacognitive awareness of the meaning and the purpose of the analogy, and their personal use of the analogy in changing initial conceptions. As hypothesized, results showed a high correlation between level of conceptual understanding of the new science topic, level of understanding of the analogy itself, and the effective use of the analogy in integrating the new information into the pre-existing conceptual structures. Some implications on the use of analogy for conceptual change are considered from an educational standpoint. 相似文献
14.
Model fit indices are being increasingly recommended and used to select the number of factors in an exploratory factor analysis. Growing evidence suggests that the recommended cutoff values for common model fit indices are not appropriate for use in an exploratory factor analysis context. A particularly prominent problem in scale evaluation is the ubiquity of correlated residuals and imperfect model specification. Our research focuses on a scale evaluation context and the performance of four standard model fit indices: root mean square error of approximate (RMSEA), standardized root mean square residual (SRMR), comparative fit index (CFI), and Tucker–Lewis index (TLI), and two equivalence test-based model fit indices: RMSEAt and CFIt. We use Monte Carlo simulation to generate and analyze data based on a substantive example using the positive and negative affective schedule (N = 1,000). We systematically vary the number and magnitude of correlated residuals as well as nonspecific misspecification, to evaluate the impact on model fit indices in fitting a two-factor exploratory factor analysis. Our results show that all fit indices, except SRMR, are overly sensitive to correlated residuals and nonspecific error, resulting in solutions that are overfactored. SRMR performed well, consistently selecting the correct number of factors; however, previous research suggests it does not perform well with categorical data. In general, we do not recommend using model fit indices to select number of factors in a scale evaluation framework. 相似文献
15.
Ji Hoon Ryoo Timothy R. Konold Jeffrey D. Long Victoria J. Molfese Xin Zhou 《Structural equation modeling》2017,24(6):897-910
Applications of growth mixture modeling have become widespread in the fields of medicine, public health, and the social sciences for modeling linear and nonlinear patterns of change in longitudinal data with presumed heterogeneity with respect to latent group membership. However, in contrast to linear approaches, there has been relatively less focus on methods for modeling nonlinear change. We introduce a nonlinear mixture modeling approach for estimating change trajectories that rely on the use of fractional polynomials within a growth mixture modeling framework. Fractional polynomials allow for more parsimonious and flexible models in comparison to conventional polynomial models. The procedures are illustrated through the use of math ability scores obtained from 499 children over a period of 3 years, with 4 measurement occasions. Techniques for identifying the best empirically derived growth mixture model solution are also described and illustrated by way of substantive example and a simulation. 相似文献
16.
The cohort growth model (CGM) is a method for estimating the parameters of a latent growth model (LGM) based on cross-sectional data. The CGM models the interindividual differences in the growth rate, and it models how subjects’ growth rate is related to their initial status. We derive model identification for the CGM and illustrate, in a simulation study, that the CGM provides unbiased parameter estimates in most simulation conditions. Based on empirical data we compare the estimates of the CGM with the estimates of the LGM. The results were comparable for both models. Although the estimates of the (co)-variances were different, the estimates of both models led to similar conclusions on the developmental change. Finally, we discuss the advantages and limitations of the CGM, and we provide recommendations for its use in empirical research. 相似文献
17.
When practitioners use modern measurement models to evaluate rating quality, they commonly examine rater fit statistics that summarize how well each rater's ratings fit the expectations of the measurement model. Essentially, this approach involves examining the unexpected ratings that each misfitting rater assigned (i.e., carrying out analyses of standardized residuals). One can create plots of the standardized residuals, isolating those that resulted from raters’ ratings of particular subgroups. Practitioners can then examine the plots to identify raters who did not maintain a uniform level of severity when they assessed various subgroups (i.e., exhibited evidence of differential rater functioning). In this study, we analyzed simulated and real data to explore the utility of this between‐subgroup fit approach. We used standardized between‐subgroup outfit statistics to identify misfitting raters and the corresponding plots of their standardized residuals to determine whether there were any identifiable patterns in each rater's misfitting ratings related to subgroups. 相似文献
18.
The purpose of this study was to examine the impact of misspecifying a growth mixture model (GMM) by assuming that Level-1 residual variances are constant across classes, when they do, in fact, vary in each subpopulation. Misspecification produced bias in the within-class growth trajectories and variance components, and estimates were substantially less precise than those obtained from a correctly specified GMM. Bias and precision became worse as the ratio of the largest to smallest Level-1 residual variances increased, class proportions became more disparate, and the number of class-specific residual variances in the population increased. Although the Level-1 residuals are typically of little substantive interest, these results suggest that researchers should carefully estimate and report these parameters in published GMM applications. 相似文献
19.
Achievement goals have been linked to achievement in various educational settings. The present work explored day-to-day variations in achievement goals (mastery, performance-approach, performance-avoidance) and their associations with daily experiences of academic success and failure. Ambulatory assessment data from 108 students in Grade 5 were collected, with daily assessments of achievement goals in the morning and end-of-day reports of academic success and failure. Dynamic structural equation models revealed reciprocal within-person effects between mastery goals and academic success. Academic success was further associated with higher mastery and performance-approach goals in the next morning. Academic failure was linked to both performance goals, though this association was not robust in all sensitivity analyses. Higher average daily academic success and lower average academic failure were linked to better academic achievement one year later. Findings suggest meaningful within-person dynamics among goals and daily academic success and failure. 相似文献
20.
Jacqueline Witschge Jesper Rözer Herman G. van de Werfhorst 《British Educational Research Journal》2019,45(2):298-319
In addition to increasing cognitive skills and preparing students for the labour market, one of the core tasks of education is to prepare citizens for participation in democracy. Considering the ideal of democratic equality, it is important to know the degree to which civic outcomes of education are distributed equally. One feature of the education system that can lead to differential civic outcomes is tracking, that is, the sorting of students into different types of education. In this study, we examine the relationship between type of education (general/academic or vocational) and five attitudinal dimensions of civic and political engagement between the ages of 14 and 49 years in the Netherlands. By using panel data from the Netherlands Longitudinal Lifecourse Study (n = 5,312) and applying linear fixed effects models, we can observe the effect of a transition in the type of education on the within-person change in our outcome variables. The findings demonstrate that transitions in the type of education have little effect on intention to vote, trust in institutions or ethnic tolerance. However, students making transitions in general/academic education develop higher levels of interest in politics and generalised trust than do students in vocational education or people outside the education system. This point suggests that general/academic education fosters civic and political participation. 相似文献