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1.
The main purpose of this paper is to demonstrate how to apply the Hierarchical Linear Modeling (HLM) technique to multi-wave
Curriculum-Based Measurement (CBM) measures in modeling academic growth and assessing its relations to student- and instruction-related
variables. HLM has advantages over other statistical methods (e.g., repeated measures ANOVA, Structural Equation Modeling)
in modeling academic growth. The advantages include allowing more flexible research designs in collecting multiple data points
and estimating growth rates and their relations to correlates in more reliable, accurate ways. CBM, as a multi-wave progressmonitoring
system, also has distinctive psychometric features that facilitate longitudinal research on academic skill development. These
features include provision of multiple data points within short time periods, good validity and reliability, and sensitivity
for detecting small degrees of change. Finally, research questions related to assessing the academic growth of students with
learning difficulties and using assessment results to improve educational practices for them are discussed 相似文献
2.
Fuzhong Li Terry E. Duncan Peter Harmer Alan Acock Mike Stoolmiller 《Structural equation modeling》2013,20(3):294-306
Confirmatory factor analysis (CFA) is often used in the social sciences to estimate a measurement model in which multiple measurement items are hypothesized to assess a particular latent construct. This article presents the utility of multilevel CFA (MCFA; Muthén, 1991, 1994) and hierarchical linear modeling (HLM; Raudenbush, Rowan, & Kang, 1991) methods in testing measurement models in which the underlying attribute may vary as a function of various levels of observation. An illustrative example using a real dataset is provided in which an unconditional model specification and parameter estimates from the MCFA and HLM are shown. The article demonstrates the comparability of the two methods in estimating measurement parameters of interest (i.e., true variance at levels the measures are used and measurement errors). 相似文献
3.
Growth mixture modeling (GMM) is a useful statistical method for longitudinal studies because it includes features of both latent growth modeling (LGM) and finite mixture modeling. This Monte Carlo simulation study explored the impact of ignoring 3 types of time series processes (i.e., AR(1), MA(1), and ARMA(1,1)) in GMM and manipulated the separation of the latent classes, the strength of the time series process, and whether the errors conformed to the time series process in 1 or 2 latent classes. The results showed that omitting time series processes resulted in more serious bias in parameter estimation as the distance between classes increased. However, when the class distances were small, ignoring time series processes contributed to the selection of the correct number of classes. When the GMM models correctly specified the time series process, only models with an AR(1) time series process produced unbiased parameter estimates in most conditions. It was also found that among design factors manipulated, the distance between classes prominently affected the identification of the number of classes and parameter estimation. 相似文献
4.
This article investigates three types of stage-sequential growth mixture models in the structural equation modeling framework for the analysis of multiple-phase longitudinal data. These models can be important tools for situations in which a single-phase growth mixture model produces distorted results and can allow researchers to better understand population heterogeneity and growth over multiple phases. Through theoretical and empirical comparisons of the models, the authors discuss strategies with respect to model selection and interpreting outcomes. The unique attributes of each approach are illustrated using ecological momentary assessment data from a tobacco cessation study. Transitional discrepancy between phases as well as growth factors are examined to see whether they can give us useful information related to a distal outcome, abstinence at 6 months postquit. It is argued that these statistical models are powerful and flexible tools for the analysis of complex and detailed longitudinal data. 相似文献
5.
《International Journal of Research & Method in Education》2013,36(3):285-308
As applications of multilevel modelling in educational research increase, researchers realize that multilevel data collected in many educational settings are often not purely nested. The most common multilevel non-nested data structure is one that involves student mobility in longitudinal studies. This article provides a methodological review of three statistical methods for handling student mobility in longitudinal studies: a multilevel approach, a cross-classified approach, and a cross-classified multiple membership approach. The strengths and weaknesses of each approach and the essential differences between the three approaches are discussed. The Early Childhood Longitudinal Study Kindergarten Cohort data are analysed to demonstrate the differences in parameter estimates and statistical inference between the three approaches. Potential applications of the three approaches in educational research and beyond and directions for further methodological investigations are discussed. 相似文献
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.
Latent growth modeling (LGM) is a popular and flexible technique that may be used when data are collected across several different measurement occasions. Modeling the appropriate growth trajectory has important implications with respect to the accurate interpretation of parameter estimates of interest in a latent growth model that may impact educational policy decisions. A Monte Carlo simulation study was conducted to examine the accuracy of six information-based criteria (i.e., AIC, CAIC, AICC, BIC, nBIC, and HQIC) when selecting among various growth trajectories modeled using LGM under different sample size, number of time points, and growth trajectory scenarios. The accuracy of the information criteria generally improved as sample size increased. The cubic and linear growth models were distinguished most accurately by the information criteria. All of the nonlinear models were more easily distinguished as the number of time points increased. The comparative performance of the six information criteria was dependent upon the manipulated conditions. Implications of the findings are discussed. 相似文献
8.
This article compares two statistical approaches for modeling growth across time. The two statistical approaches are the multilevel model (MLM) and latent curve analysis (LCA), which have been proposed to depict change or growth adequately. These two approaches were compared in terms of the estimation of growth profiles represented by the parameters of initial status and the rate of growth. A longitudinal data set obtained from a school‐based substance‐use prevention trial for adolescents was used to illustrate the similarities and differences between the two approaches. The results indicated that the two approaches yielded very compatible results. The parameter estimates associated with regression weights are the same, whereas those associated with variances and covariances are similar. The MLM approach is easier for model specification and is more efficient computationally in yielding results. The LCA approach, however, has the advantage of providing model evaluation, that is, an overall test of goodness of fit, and is more flexible in modeling and hypothesis testing as demonstrated in this study. 相似文献
9.
JeeWon Cheong 《Structural equation modeling》2013,20(2):195-211
The latent growth curve modeling (LGCM) approach has been increasingly utilized to investigate longitudinal mediation. However, little is known about the accuracy of the estimates and statistical power when mediation is evaluated in the LGCM framework. A simulation study was conducted to address these issues under various conditions including sample size, effect size of mediated effect, number of measurement occasions, and R 2 of measured variables. In general, the results showed that relatively large samples were needed to accurately estimate the mediated effects and to have adequate statistical power, when testing mediation in the LGCM framework. Guidelines for designing studies to examine longitudinal mediation and ways to improve the accuracy of the estimates and statistical power were discussed. 相似文献
10.
Madorah E. Smith 《Journal of Experimental Education》2013,81(2):121-132
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
11.
Models of change typically assume longitudinal measurement invariance. Key constructs are often measured by ordered-categorical indicators (e.g., Likert scale items). If tests based on such indicators do not support longitudinal measurement invariance, it would be useful to gauge the practical significance of the detected non-invariance. The authors focus on the commonly used second-order latent growth curve model, proposing a sensitivity analysis that compares the growth parameter estimates from a model assuming the highest achieved level of measurement invariance to those from a model assuming a higher, incorrect level of measurement invariance as a measure of practical significance. A simulation study investigated the practical significance of non-invariance in different locations (loadings, thresholds, uniquenesses) in second-order latent linear growth models. The mean linear slope was affected by non-invariance in the loadings and thresholds, the intercept variance was affected by non-invariance in the uniquenesses, and the linear slope variance and intercept–slope covariance were affected by non-invariance in all three locations. 相似文献
12.
This study investigated the development of academic self-concept and language achievement from Grade 7 to Grade 12 by repeated assessment of 2826 Flemish adolescents in 50 secondary schools. Latent growth curve modeling showed that both girls and boys experience a declining academic self-concept during the period of secondary education and that girls declined at a faster rate. Furthermore, girls were shown to have an increase in Dutch language achievement over time, whereas boys showed a decrease in middle years, followed by an increase from Grade 9 on. The multivariate multilevel growth curve model suggested that the evolution of academic self-concept was not related to the evolution in achievement, neither at the individual level, nor at the school level. There is, however, a positive relation between students’ academic self-concept and their achievement, the magnitude of which decreased throughout secondary school. At the school level, the correlation is small, but also positive, except for the girls from Grade 10 on. The results are discussed in relation to the reciprocal effects model and the developmental perspective regarding the self-concept/achievement relation. 相似文献
13.
Walter L. Leite Robert Sandbach Rong Jin Jann W. MacInnes M. Grace-Anne Jackman 《Structural equation modeling》2013,20(3):437-456
Because random assignment is not possible in observational studies, estimates of treatment effects might be biased due to selection on observable and unobservable variables. To strengthen causal inference in longitudinal observational studies of multiple treatments, we present 4 latent growth models for propensity score matched groups, and evaluate their performance with a Monte Carlo simulation study. We found that the 4 models performed similarly with respect to model fit, bias of parameter estimates, Type I error, and power to test the treatment effect. To demonstrate a multigroup latent growth model with dummy treatment indicators, we estimated the effect of students changing schools during elementary school years on their reading and mathematics achievement, using data from the Early Childhood Longitudinal Study Kindergarten Cohort. 相似文献
14.
This Monte Carlo study investigated the impacts of measurement noninvariance across groups on major parameter estimates in latent growth modeling when researchers test group differences in initial status and latent growth. The average initial status and latent growth and the group effects on initial status and latent growth were investigated in terms of Type I error and bias. The location and magnitude of noninvariance across groups was related to the location and magnitude of bias and Type I error in the parameter estimates. That is, noninvariance in factor loadings and intercepts was associated with the Type I error inflation and bias in the parameter estimates of the slope factor (or latent growth) and the intercept factor (or initial status), respectively. As noninvariance became large, the degree of Type I error and bias also increased. On the other hand, a correctly specified second-order latent growth model yielded unbiased parameter estimates and correct statistical inferences. Other findings and implications on future studies were discussed. 相似文献
15.
Appropriate model specification is fundamental to unbiased parameter estimates and accurate model interpretations in structural equation modeling. Thus detecting potential model misspecification has drawn the attention of many researchers. This simulation study evaluates the efficacy of the Bayesian approach (the posterior predictive checking, or PPC procedure) under multilevel bifactor model misspecification (i.e., ignoring a specific factor at the within level). The impact of model misspecification on structural coefficients was also examined in terms of bias and power. Results showed that the PPC procedure performed better in detecting multilevel bifactor model misspecification, when the misspecification became more severe and sample size was larger. Structural coefficients were increasingly negatively biased at the within level, as model misspecification became more severe. Model misspecification at the within level affected the between-level structural coefficient estimates more when data dependency was lower and the number of clusters was smaller. Implications for researchers are discussed. 相似文献
16.
Su-Young Kim 《Structural equation modeling》2013,20(3):457-476
Just as growth mixture models are useful with single-phase longitudinal data, multiphase growth mixture models can be used with multiple-phase longitudinal data. One of the practically important issues in single- and multiphase growth mixture models is the sample size requirements for accurate estimation. In a Monte Carlo simulation study, the sample sizes required for using these models are investigated under various theoretical and realistic conditions. In particular, the relationship between the sample size requirement and the number of indicator variables is examined, because the number of indicators can be relatively easily controlled by researchers in many multiphase data collection settings such as ecological momentary assessment. The findings not only provide tangible information about required sample sizes under various conditions to help researchers, but they also increase understanding of sample size requirements in single- and multiphase growth mixture models. 相似文献
17.
Tacksoo Shin 《Asia Pacific Education Review》2012,13(1):65-76
This study introduced various nonlinear growth models, including the quadratic conventional polynomial model, the fractional
polynomial model, the Sigmoid model, the growth model with negative exponential functions, the multidimensional scaling technique,
and the unstructured growth curve model. It investigated which growth models effectively describe student growth in math and
reading using four-wave longitudinal achievement data. The objective of the study is to provide valuable information to researchers
especially when they consider applying one of the nonlinear models to longitudinal studies. The results showed that the quadratic
conventional polynomial model fit the data best. However, this model seemed to overfit the data and made statistical inference
problematic concerning parameter estimates. Alternative nonlinear models with fewer parameters adequately fit the data and
yielded consistent significance testing results under extreme multicollinearity. It indicates that the alternative models
denoting somewhat simpler models would be selected over the conventional polynomial model with more fixed parameters. Other
practical issues pertaining to these growth models are also discussed. 相似文献
18.
Huy Phuong Phan 《教育心理学》2010,30(5):547-564
This study used latent growth modelling (LGM) to explore the developmental course and longitudinal relationships between achievement goals (mastery and performance‐approach) and academic performance over a three‐year period (four time‐points of data collection). Three hundred and fifty‐two university students (152 women, 200 men) who first enrolled in 2006 took part in this study. Likert‐scale inventories were used to elicit relevant data from students. Academic performance was collated from students' course and final exam marks in two different undergraduate courses. LISREL 8.72 and SPSS 17 were used to test and evaluate the conceptual model proposed. Causal modelling analyses indicated the temporally displaced effects of mastery and performance‐approach goals on academic performance. The results indicated that individuals' mastery goals increased over time, whereas there was no increase in growth change with performance‐approach goals. Causal modelling also indicated: (1) performance‐approach goals → academic performance → mastery goals relationship and (2) mastery goals → academic performance → mastery goals relationship. Finally, the use of LGM provided a clearer perspective concerning the developmental trajectories of mastery goals over time. 相似文献
19.
This study discusses the effects of oversimplifying the between-subject covariance structure on inferences for fixed effects in modeling nested data. Linear and quadratic growth curve models (GCMs) with both full and simplified between-subject covariance structures were fit to real longitudinal data. The results were contradictory to the statement that using oversimplified between-subject covariance structures (e.g., uni-level analysis) leads to underestimated standard errors of fixed effect estimates and thus inflated Type I error rates. We analytically derived simple mathematical forms to systematically examine the oversimplification effects for the linear GCMs. The derivation results were aligned with the real data analysis results and further revealed the conditions under which the standard errors of the fixed-effect intercept and slope estimates could be underestimated or overestimated for over-simplified linear GCMs. Therefore, our results showed that the underestimation statement is a myth and can be misleading. Implications are discussed and recommendations are provided. 相似文献
20.
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