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  • Scaling methods of second-order latent growth models and their comparable first-order latent growth models

    Subjects: Other Disciplines >> Synthetic discipline submitted time 2023-10-09 Cooperative journals: 《心理学报》

    Abstract: Latent growth models (LGMs) are a powerful tool for analyzing longitudinal data, and have attracted the attention of scholars in psychology and other social science disciplines. For a latent variable measured by multiple indicators, we can establish both a univariate LGM (also called first-order LGM) based on composite scores and a latent variable LGM (also called second-order LGM) based on indicators. The two model types are special cases of the first-order and second-order factor models respectively. In either case, we need to scale the factors, that is, to specify their origin and unit. Under the condition of strong measurement invariance across time, the estimation of growth parameters in second-order LGMs depends on the scaling method of factors/latent variables. There are three scaling methods: the scaled-indicator method (also called the marker-variable identification method), the effect-coding method (also called the effect-coding identification method), and the latent-standardization method. The existing latent-standardization method depends on the reliability of the scaled-indicator or the composite scores at the first time point. In this paper, we propose an operable latent-standardization method with two steps. In the first step, a CFA with strong measurement invariance is conducted by fixing the mean and variance of the latent variable at the first time point to 0 and 1 respectively. In the second step, estimated loadings in the first step are employed to establish the second-order LGM. If the standardization is based on the scaled-indicator method, the loading of the scaled-indicator is fixed to that obtained in the first step, and the intercept of the scaled-indicator is fixed to the sample mean of the scaled-indicator at the first time point. If the standardization is based on the effect-coding method, the sum of loadings is constrained to the sum of loadings obtained in the first step, and the sum of intercepts is constrained to the sum of the sample mean of all indicators at the first time point. We also propose a first-order LGM standardization procedure based on the composite scores. First, we standardize the composite scores at the first time point, and make the same linear transformation of the composite scores at the other time points. Then we establish the first-order LGM, which is comparable with the second-order LGM scaled by the latent-standardization method. The scaling methods of second-order LGMs and their comparable first-order LGMs are systematically summarized. The comparability is illustrated by modeling the empirical data of a Moral Evasion Questionnaire. For the scaled-indicator method, second-order LGMs and their comparable first-order LGMs are rather different in parameter estimates (especially when the reliability of the scale-indicator is low). For the effect-coding method, second-order LGMs and their comparable first-order LGMs are relatively close in parameter estimates. When the latent variable at the first time point is standardized, the mean of the intercept-factor of the first-order LGM is close to 0 and not statistically significant; so is the mean of the intercept-factor of the second-order LGM through the effect-coding method, but those through two scaled-indicator methods are statistically significant and different from each other. According to our research results, the effect-coding method is recommended to scale and standardize the second-order LGMs, then comparable first-order LGMs are those based on the composite scores and their standardized models. For either the first-order or second-order LGM, the standardized results obtained by modeling composite total scores and composite mean scores are identical.

  • Scaling methods of second-order latent growth models and their comparable first-order latent growth models

    Subjects: Psychology >> Statistics in Psychology submitted time 2023-03-29

    Abstract:

    Latent growth models (LGMs) are a powerful tool for analyzing longitudinal data, and have attracted the attention of scholars in psychology and other social science disciplines. For a latent variable measured by multiple indicators, we can establish both a univariate LGM (also called first-order LGM) based on composite scores and a latent variable LGM (also called second-order LGM) based on indicators. The two model types are special cases of the first-order and second-order factor models respectively. In either case, we need to scale the factors, that is, to specify their origin and unit. Under the condition of strong measurement invariance across time, the estimation of growth parameters in second-order LGMs depends on the scaling method of factors/latent variables. There are three scaling methods: the scaled-indicator method (also called the marker-variable identification method), the effect-coding method (also called the effect-coding identification method), and the latent-standardization method.

    The existing latent-standardization method depends on the reliability of the scaled-indicator or the composite scores at the first time point. In this paper, we propose an operable latent-standardization method with two steps. In the first step, a CFA with strong measurement invariance is conducted by fixing the mean and variance of the latent variable at the first time point to 0 and 1 respectively. In the second step, estimated loadings in the first step are employed to establish the second-order LGM. If the standardization is based on the scaled-indicator method, the loading of the scaled-indicator is fixed to that obtained in the first step, and the intercept of the scaled-indicator is fixed to the sample mean of the scaled-indicator at the first time point. If the standardization is based on the effect-coding method, the sum of loadings is constrained to the sum of loadings obtained in the first step, and the sum of intercepts is constrained to the sum of the sample mean of all indicators at the first time point. We also propose a first-order LGM standardization procedure based on the composite scores. First, we standardize the composite scores at the first time point, and make the same linear transformation of the composite scores at the other time points. Then we establish the first-order LGM, which is comparable with the second-order LGM scaled by the latent-standardization method.

    The scaling methods of second-order LGMs and their comparable first-order LGMs are systematically summarized. The comparability is illustrated by modeling the empirical data of a Moral Evasion Questionnaire. For the scaled-indicator method, second-order LGMs and their comparable first-order LGMs are rather different in parameter estimates (especially when the reliability of the scale-indicator is low). For the effect-coding method, second-order LGMs and their comparable first-order LGMs are relatively close in parameter estimates. When the latent variable at the first time point is standardized, the mean of the intercept-factor of the first-order LGM is close to 0 and not statistically significant; so is the mean of the intercept-factor of the second-order LGM through the effect-coding method, but those through two scaled-indicator methods are statistically significant and different from each other.  

    According to our research results, the effect-coding method is recommended to scale and standardize the second-order LGMs, then comparable first-order LGMs are those based on the composite scores and their standardized models. For either the first-order or second-order LGM, the standardized results obtained by modeling composite total scores and composite mean scores are identical.

  • 基于结构方程模型的多层调节效应

    Subjects: Psychology >> Developmental Psychology submitted time 2023-03-28 Cooperative journals: 《心理科学进展》

    Abstract: In recent years, multilevel models (MLM) have been frequently used for studying multilevel moderation in social sciences. However, there still exist sampling errors and measurement errors even after separating the between-group effects from the within-group effects of multilevel moderation. To solve this problem, a new method has been developed abroad by integrating MLM with structural equation models (SEM) under the framework of multilevel structural equation models (MSEM) to set latent variables and multiple indicators. It has been showed that the method could rectify sampling errors and measurement errors effectively and obtain more accurate estimation of moderating effects. After introducing the new method by modeling with random coefficient prediction and with latent moderated structural equations, we propose a procedure for analyzing multilevel moderation by using MSEM. An example is illustrated with the software Mplus. Totally 29 articles, published in Chinese psychological journals from 2010 to 2017, are reviewed for evaluating the situation of using multilevel moderation analysis methods in psychological researches in China. Directions for future study on multilevel moderation and MSEM were discussed at the end of the paper.

  • 纵向数据的调节效应分析

    Subjects: Psychology >> Social Psychology submitted time 2023-03-28 Cooperative journals: 《心理科学进展》

    Abstract: At present, the analysis of moderating effect is mainly based on cross sectional data. This article discusses how to analyze the moderating effect with longitudinal data. If the independent variable X and the dependent variable Y are longitudinal data, longitudinal moderation models can be divided into three categories according to the type of moderator: time-invariant moderator, time-variant moderator, and moderator generated from X or Y. For example, Xtj is divided into two parts, time-varying intra-individual differences Xtj−X¯∙jXtj−X¯∙jX_{t j}-\bar{X}_{\bullet} j and time-invariant inter-individual differencesX¯∙jX¯∙j\bar{X}_{\boldsymbol{\bullet} j}, and then the moderating effect of X¯∙jX¯∙j\bar{X}_{\boldsymbol{\bullet} j} on the relationship between (Xtj−X¯∙j)(Xtj−X¯∙j)(X_{t j}-\bar{X}_{\bullet} j) and Ytj can be analyzed. In that case, there will be no new moderator Z, which is characteristic of moderation research on longitudinal data in contrast to research on cross-sectional data. Four types of longitudinal moderation analysis approaches are summarized: 1) Multilevel model (MLM); 2) Multilevel structural equation model (MSEM); 3) Cross-lagged model (CLM); 4) Latent growth model (LGM). It is found that the decomposition of the moderating effect and the use of the latent moderating structural equation (LMS) method are the two characteristics of the moderation analysis for longitudinal data. Specifically, MLM, MSEM, and CLM divide the moderating effect of longitudinal data into three parts: the time-varying intra-individual part, time-invariant inter-individual part, and the cross-level part. In addition, the moderating effect of longitudinal data can be decomposed into the moderating effect of initial level and rate of change by LGM. In the present study, we propose a procedure to analyze longitudinal mediation analysis. The first step is to decide whether it is necessary to make a causal inference. If the aim of research is to make a causal inference, CLM should be adopted to analyze longitudinal moderation. Otherwise, proceed with the second step. The second step is to decide whether it is necessary to treat longitudinal data as multilevel data. If longitudinal data is treated as multilevel data, MSEM should be adopted to analyze longitudinal moderation, because MSEM and MLM are more suitable for describing individual differences. Otherwise, LGM should be adopted to analyze longitudinal moderation, because only an LGM can simultaneously examine the effect of some variables on change and how the change affects other variables. The third step is to decide whether MSEM converges. If MSEM converges, the result of MSEM should be reported. Otherwise, MLM should be adopted to analyze longitudinal moderation. Compared with MLM, MSEM takes sampling error into account when the group mean is calculated, but the convergence of the MSEM is more difficult. Therefore, the MSEM with sampling error taken into account is preferred. If convergence fails, MLM will be considered. This paper exemplifies how to conduct the proposed procedure by using Mplus. Directions for future research on moderation analysis of longitudinal data are discussed, such as the moderation analysis for intensive longitudinal data based on the dynamic structural equation model.

  • 追踪研究中的内生性问题:来源与应对

    Subjects: Psychology >> Social Psychology submitted time 2023-03-28 Cooperative journals: 《心理科学进展》

    Abstract: Longitudinal cross-lagged models have been widely used to analyze causal relations in behavioral and psychological sciences, and the cross-lagged panel model (CLPM) is common and important. The CLPM and related panel data models usually consist of two kinds of regression relations: (a) the autoregressive effects of a variable from its prior state (an earlier time point) to its current state (present time point) and (b) the cross-lagged effects of one variable at the prior state to another variable at the current state. These effects between the two constructs provide the foundation and crucial information in deciding on their diachronic causation. Importantly, in contrast to general regression models, a CLPM consists of a complex set of regression equations, making it more susceptible to endogeneity-related problems.Endogeneity is a critical concern in regression analyses, which refers to situations when an explanatory variable is correlated with the residual (error) of its regression equation. It will likely lead to over- or under-estimated bias with commonly used estimators. Endogeneity is a critical concern when using regression models to analyze observational data to make causal claims. The CLPM determines diachronic causation based on two kinds of regression effects (autoregressive and cross-lagged paths). Despite its vulnerability to endogeneity, this issue has received little attention and requires systematic analyses.The current study focuses on issues related to endogeneity in the CLPM. We first clarify the main sources of endogeneity problems. Then, we systematically analyze different endogeneity issues in the CLPM. Lastly, we provide an empirical example to illustrate the use of the instrumental variables (IV) method in the CLPM.IV originates from econometrics and refers to the predictor of a predictor. The IV method is probably the most popular approach while dealing with endogeneity. Researchers often incorporate suitable IVs in the model to provide unbiased estimates and alleviate the endogeneity concerns. The model implied IVs (MIIVs) have been frequently used in empirical studies. A MIIV is an IV identified within the model. The MIIVs offer a promising way to deal with endogeneity in longitudinal analyses. Typically, a MIIV is a chronologically prior observation of an exogenous variable in the model. Currently, applications with IV are underutilized in psychological research. This paper tries to illustrate the use of MIIV in the CLPM by an empirical example. To our knowledge, this is the first study to discuss endogeneity issues in the CLPM and explore the performances of MIIV in the longitudinal cross-lagged model. We find that common possible sources of endogeneity in the CLPM are: omitted variables, dynamic panel, and reciprocal relation. The omitted variables are ubiquitous in all empirical research and the omitted variable problem will affect the estimation of cross-lagged analyses. For the dynamic panel, “dynamic” refers to the use of the prior outcome as a predictor. Including the effects of this lagged outcome increases the probability of the explanatory variable being related to the residual. Besides, biases could arise from the reciprocal relation, which is also known as the feedback relation, simultaneity, or simultaneous causality. We conclude, first, there are various types of endogeneity in the CLPM, including the omitted variables, dynamic panel, and reciprocal relation. Second, endogeneity could distort the estimation of cross-lagged effects in the CLPM. Lastly, MIIV is a promising technique to tackle endogeneity issues in the CLPM. For future research, it would be interesting to explore the performance of MIIV in models extended from the CLPM. They may include the Random Intercept-CLPM, the Latent Cure Model with Structured Residuals (LCM-SR), and the Latent Change Score Model (LCS).This paper reviews the main sources of endogeneity in the CLPM to raise applied researchers' awareness of the endogeneity issues in longitudinal research. We recommend the MIIV-CLPM as a solution to deal with the endogeneity issue.

  • 新世纪20年国内心理统计方法研究回顾

    Subjects: Psychology >> Social Psychology submitted time 2023-03-28 Cooperative journals: 《心理科学进展》

    Abstract: A total of 213 articles on psychological statistical methods have been published in 11 journals of psychology in Mainland China from 2001 to 2020. There are mainly 10 areas attractive to researchers (sorted by the number of papers): structural equation models (SEM), test reliability, mediation effect, effect size and testing power, longitudinal study, moderation effect, exploratory factor analysis, latent class analysis, common method bias and hierarchical linear models. Research on structural equation models (with confirmatory factor analysis model as a special case) explore five major aspects: model fit evaluation, model estimation, item parceling, measurement invariance and the extensions of SEM. The last aspect includes exploratory structural equation modeling, factor mixture modeling, high-order factor modeling as well as bifactor modeling. Articles on exploratory factor analysis focus on factor extraction. Modern reliability analysis is inextricably linked with factor models, including three main topics: distinction between coefficientα and internal consistency or homogeneity, confidence interval estimation of composite reliability and homogeneity coefficient, and reliability of multilevel data and longitudinal data. Common method bias is also based on factor analysis and studied in three aspects: the relationship between common method bias and common method variance, the influence of common method bias, and the comparison of approaches for testing and controlling common method bias. Studies on mediation effects can be summarized in four topics: testing approaches and their comparison, mediation effect size, mediation effect testing for categorical variables, and the extensions of mediation models. The simple mediation model was extended to multilevel or multiple mediation models, moderated mediation models and mediated moderation models, as well as mediation models of longitudinal data. Articles on moderation effects mainly explore three issues: the development of latent interaction models from those with mean structure to those without mean structure, and the change from latent interaction models with product indicators to those without product indicators, as well as standardized estimates of latent moderating effect models. Articles on longitudinal data analysis fall into three main groups. The first is the development of models, which includes hierarchical linear models, latent growth models and its mixture models, piecewise growth models and its mixture models, etc. The second is the development of longitudinal data collecting methods, which include intensive longitudinal and accelerated longitudinal design. The last is missing data handing methods of longitudinal data. Hierarchical linear models were studied in three directions: aggregation adequacy testing used in aggregating the ratings of individual level to team level, hierarchical linear model of categorical variables as outcome variables (including multilevel binomial and multilevel multinomial logit models), hierarchical linear modeling of latent variables (i.e., multilevel structural equation model). Research on latent class models investigates three main topics: the use of latent class analysis, latent profile analysis and Taxometric techniques in probing latent class structure; precision of classification; regression mixture model (i.e., latent class model including covariates). Both effect size and testing power are closely associated with hypothesis testing, and studies in this area introduce types and characteristics of effect size, calculation of testing power, alternative approaches and their supplements for testing null hypothesis significance.

  • 新世纪20年国内结构方程模型方法研究与模型发展

    Subjects: Psychology >> Social Psychology submitted time 2023-03-28 Cooperative journals: 《心理科学进展》

    Abstract: Structural equation modeling (SEM) is an important statistical method in social science research. In the first two decades of the 21st century, great progress has been made in methodological research on SEM in China’s mainland. The publications cover five aspects: model development, parameter estimation, model evaluation, measurement invariance and the special data processing in SEM. SEM development includes the research on measurement models, structural models, and complete models, as well as the SEM in population heterogeneity studies and longitudinal studies. The research on the measurement models involves bi-factor model, exploratory structural equation model, measurement models for special design (e.g., random intercept factor analysis model, fixed-links model, and the Thurston model), and formative measurement models. The research on the structural models involves the actor-partner interdependence model. The research on the complete models focuses on item parceling. The SEM in the study of population heterogeneity involves latent class/profile model, factor mixture model, and multi-level latent class model. The SEM in longitudinal studies includes models describing development trajectories and differences, such as the latent growth model, the piecewise growth model, the latent class growth model, the growth mixture model, the piecewise growth mixture model, the latent transition model and the cross-lagged model. The publications on parameter estimation methods mainly involve the introduction of methodology (including the partial least square method and the Bayesian method) and the comparison of different parameter estimation methods. Advances in the model evaluation include fit indices and their corresponding critical values, selection of fit indices, model evaluation criteria beyond fit indices, and comparison and selection among alternative models. The development of measurement invariance involves three topics: (1) the introduction of different models with testing process and model evaluation criteria for measurement invariance analysis; (2) measurement invariance analysis in a particular model or data (e.g., second order factor model and ordered categorical data); (3) new methods of measurement invariance analysis (e.g., alignment and projection method). In addition, research into special data processing methods in SEM addresses issues of missing data, non-continuous data, non-normal data, and latent variable scores. Finally, recent advances in SEM methodological research abroad are introduced to help researchers understand some cutting-edge topics in this field, which offers implications for future directions of SEM methodological research.

  • 新世纪20年国内假设检验及其关联问题的方法学研究

    Subjects: Psychology >> Social Psychology submitted time 2023-03-28 Cooperative journals: 《心理科学进展》

    Abstract: Hypothesis testing is an important part of inferential statistics. Most reported statistical test results are based on the null hypothesis significance test (NHST). In the first two decades of the 21st century, the studies on hypothesis testing and related topics in China’s mainland cover such topics as the deficiency of the null hypothesis significance test, use of P-value, repeatability of psychological research, effect size, power of a statistical test, and equivalence test, among others. This systematic review summarizes the main findings and gives suggestions. NHST has a wide range of applications to a variety of fields, from mathematical statistics to psychology. In the past two decades, Chinese researchers have experienced a process from knowing, using, misunderstanding, understanding, and questioning it, to constantly proposing improvement methods. NHST still occupies an important position in scientific research, despite some shortcomings. When providing statistically significant results, it is recommended to offer precise P-values in order to better evaluate the type I error rate. When one wants to verify is equivalence (or zero effect), a better approach is to set an equivalent boundary value and put the equivalence hypothesis in the position of alternative hypothesis. NHST has been developed into a set of procedures as follows: First, to ensure the power of a statistical test and save costs, one should do a priori power analysis before sampling, and calculate the required sample size. The only exception is questionnaire studies with more than 160 participants which usually do not need such priori power analysis in the traditional statistical analysis. Second, to collect and analyze data, and report NHST results and confidence intervals. Third, to calculate and report the effect size if the results are statistically significant (at this time only the Type Ⅰ error is possible), and draw conclusions based on the magnitude of the effect size. Fourth, to calculate the effect size if the results are not statistically significant (at this time only the Type Ⅱ error is possible), and accept the null hypothesis if the effect size is small. However, a posterior power analysis is required when the effect size is medium or large. If the test power is high, the null hypothesis will be accepted; if the test power is less than 80%, more participants could be added for further analysis. The process of increasing the sample size should be reported clearly, with the final P-value presented and the type I error rate evaluated. Furthermore, the reproducibility crisis of psychological research is partly attributable to NHST. But the reproducibility of scientific research must be strictly defined. Although the failure to replicate a study may result from inaccurate operations and improper methods, it may also be caused by moderating effect. We can't judge the scientificity of a study simply by whether it is replicable. There are three major aspects for expanding the research on the related issues of hypothesis testing. Firstly, the equivalence test has been extended to the evaluation of structural equation models. Second, the analysis of test power has been extended to models other than those in traditional statistics, such as mediation effect models and structural equation models. Third, the effect size has also been extended to models other than those in traditional statistics, and a new R2-type effect size was proposed by using variance decomposition.

  • 新世纪20年国内测验信度研究

    Subjects: Psychology >> Social Psychology submitted time 2023-03-28 Cooperative journals: 《心理科学进展》

    Abstract: With the application of confirmatory factor analysis, research on reliability has entered a new stage. In the first two decades of the 21st century, the studies on test reliability (including point estimation and interval estimation) in China’s mainland show three main lines of development. The first line is the development from research centered on the coefficient αto the reliability research based on confirmatory factor models, including the homogeneity coefficient, composite reliability, maximum reliability, single-indicator reliability and reliability of the whole item set scores. Studies have shown that the coefficient αis still useful. In most cases, the α coefficient is the lower bound of the reliability of the composite score (total or average score). As long as the coefficient αis high enough, the test reliability will be even higher. But the coefficient αcannot be used to measure the homogeneity and the internal consistency of a test. The homogeneity coefficient based on the bi-factor model can be adopted to measure the homogeneity of a multidimensional scale, and the composite reliability can be adopted to measure the internal consistency (if consistency is understood as the consistency within each dimension). Furthermore, the Delta method can be employed to estimate the confidence intervals of various reliability. The second line is the expansion of data types collected by scales (or questionnaires), from single-level data to multi-level and longitudinal data. Whether unidimensional or multidimensional, it is recommended to use a multi-level confirmatory factor model to calculate the reliability of multi-level data. As for the longitudinal data, it is recommended to use the test reliability developed on the basis of the linear mixed model, and the longitudinal data can also be used as a special case of the two-level data for reliability analysis. The third line is the extended use of reliability, involving rater reliability, encoder reliability, attribute-level classification consistency in cognitive diagnostic assessment, and reliability of difference scores. In addition, research of reliability generalization and reliability meta-analysis appeared. For a common test with item-errors that can be reasonably assumed uncorrelated, the following procedure of reliability analysis is recommended. When the coefficient αis high enough, report the coefficient α; otherwise calculate the composite reliability on the basis of the factor model. If the composite reliability is high enough, report the composite reliability; otherwise the test reliability is considered unacceptable. If the composite reliability of every variable in a statistical model is very high (over 0.95), modeling with composite scores does not differ much from modeling with latent variables. Otherwise, it is better to use latent variable modeling.

  • 国内追踪数据分析方法研究与模型发展

    Subjects: Psychology >> Social Psychology submitted time 2023-03-28 Cooperative journals: 《心理科学进展》

    Abstract: Longitudinal research could systematically capture the change of the target variable and thus is more convincing than cross-sectional research. It is popular in the fields of social sciences such as psychology, management, statistics, sociology, etc. The present study reviews the methodology study and model development for analyzing longitudinal data in China’s mainland. We aim to retrospect the methods used, the main research questions, and the popular research domains in longitudinal models. The target publications ranged from 1st Jan. 2001 to 31st Dec. 2020 in CNKI core collections in the relative domains, and finally, 75 articles met our selecting criterion. Results also indicated that the research topic widely includes latent growth model, multilevel modeling, autoregression, cross-lagged model, missing data, etc. Among these research topics, latent growth model ranked as the first. Typically, the latent growth model and experience sampling method were favored in the field of psychology. There are mainly four research questions retrieved from the publications. The first research question is to compare the mean difference, which is less popular. The second research question is to examine the reciprocal relationship between variables. It often uses the cross-lag model and the causal model to reveal the autoregressive and cross-lagged relationships within and between variables. The third research question is to depict growth trajectory with individual differences. It uses the latent growth model (LGM) and multilevel model (MLM) as the main methods to show a growth trajectory from the between-person perspective, as well as the individual difference included. The last one is to explore the dynamic changes. This research question does not focus on the general tendency of change but on the fluctuation between different time points. It usually uses autoregression with its extensions, MLM, time-varying effect model, and some newly developed models such as the dynamic structural equation model. The recent 20 years' publication broadens the domains of longitudinal models, such as the extension of the shape and pattern of growth, the combination of latent class analysis leading to growth mixture model and latent transition analysis. The causal effect, longitudinal mediation and moderation models are also introduced to reveal the relationship between variables. Meanwhile, models depicting growth trajectory with individual differences combines with models examining reciprocal relationships, thus they were extended and integrated to random intercept cross-lagged model, latent variable autoregressive latent trajectory, as well as general cross lagged model. Furthermore, research design becomes more complex; the intensive longitudinal data was introduced and thus the models were according developed, such as MLM, time-varying effect model, dynamic structural equation model, group iterative multiple model estimation, and so forth. Particularly, missing data issue is also hot discussed in the field. To summarize, methodology study for analyzing longitudinal data in China’s mainland has made fruitful development on the above topics and are in an advanced position all over the world. However, when comparing to the international scope, publications in China’s mainland are limited in narrow range. Many topics need to keep up with the international pace, which is a direction that Chinese scholars need to make efforts. Another future direction is to learn from other disciplines to promote the development of interdisciplinary.

  • 国内中介效应的方法学研究

    Subjects: Psychology >> Social Psychology submitted time 2023-03-28 Cooperative journals: 《心理科学进展》

    Abstract: Being able to analyze the influence mechanism of independent variables on dependent variables, the analysis of mediation effect has become an important statistical method in multivariate research. Since the first publication of Chinese paper on the mediation effect and its analytical methods in 2004, the mediation effect has become one focus of methodological research in Chinese Mainland, which is systematically reviewed in this paper. Firstly, the simple mediation model is reviewed with concept identification: how to distinguish between mediation and suppression effects, partial and complete mediation effects, and mediation effect and moderation effect. Then, methodological research on mediation effects in China’s Mainland is divided into five aspects: testing method for mediation effects, mediation effect size measure, mediation effect involving categorical variables or longitudinal data, and extended mediation model. They are summarized as follows. To test ab≠0,the easiest way is to test a≠0 and b≠0. These sequential tests are actually not the same as the joint significance tests because the Type-I error rates are rather different. If the test result is a≠0 and b≠0, then ab≠0 can be inferred with the Type-I error rate less than the significance level 0.05 (the preset significance level), while the Type-I error rate of the joint significance tests is 0.0975. However, if at least one of a≠0 and b≠0 does not hold, the sequential tests should not be used, since its statistical power is less than other alternative test methods discussed in the paper. Anyway, Bootstrap methods are preferred because they provide interval estimation of the mediation effect with a higher power. Furthermore, if appropriate prior information is available, the Bayesian method is also recommended. It is believed that κ2, R2-type and so on are not suitable as mediation effect size measures because of no monotonicity. Although υ=(ab)2υ=(ab)2\upsilon ={{(ab)}^{2}} is monotonic, it is not as simple and clear as the mediation effect (ab) itself. It is recommended that when the signs of ab and c are consistent, the standardized estimation of ab and ab/c should be reported. Mediation analysis with multi-categorical independent variables and with a two-condition within-participant design are discussed when categorical variables are concerned in mediation effect models. There are two types of model development in mediation analysis with longitudinal data. One is continuous time model and multilevel time-varying coefficient model that could be used to test time-varying effect of mediation effect. The other is random-effects cross-lagged panel model and multilevel autoregressive mediation model that could be adopted to examine individuals-varying effect of mediation effect. In addition, latent growth mediation model or multilevel mediation model in mediation effect analysis could be adopted only when the involved causal relationship is instant. Otherwise, cross-lagged panel model, continuous time model, or multilevel autoregressive mediation model should be adopted. The extensions of the mediation model include multiple mediation model, multilevel mediation model, single-level and multilevel moderated mediation model as well as mediated moderation model. These extended models can be used for both the analysis of observed variables and latent variables. Finally, the recent development of foreign methodological research on mediation effects is discussed, including potential outcome mediation analysis, confounder control in mediation analysis, robust mediation analysis, and power analysis of mediation effects. Moreover, integration of new statistical techniques has become a new feature of methodological research of mediation effects, for example, exploratory mediation analysis via regularization, bi-factor mediation analysis, latent class mediation analysis, and network mediation analysis.

  • 国内调节效应的方法学研究

    Subjects: Psychology >> Social Psychology submitted time 2023-03-28 Cooperative journals: 《心理科学进展》

    Abstract: The analysis of moderation effects has become an important statistical method in multivariate studies. Methodological research on moderation effects in China’s mainland covers the following topics: moderation effects of observed variables, latent variables, multi-level data and longitudinal data; the single-level moderation effect analysis based on a two-level regression model; the integration model of moderation and mediation (see Wen et al. 2022). Methodological research on the moderation effect of observed variables includes three aspects: standardized resolution, simple slope test, and the moderation effect of category variables. The research on latent moderation includes three aspects too: standardized resolution, model simplification, and comparison of analytical methods. Under the normal condition, latent moderated structural equations (LMS) are recommended to estimate the moderation effect of latent variables. Otherwise, after centralizing all indicators, the unconstrained product indicator method is recommended to establish a latent moderation model; Bayesian method is an alternative, especially in the case of a small sample. The model development of multilevel moderation effect involves the conflated multilevel model, unconflated multilevel model (UMM), and multilevel structural equation model (MSEM). All independent variables at Level-1 are not centered in the conflated multilevel model, whereas in the UMM all independent variables at level-1 are centered using group-mean, and the group mean is included at Level-2. If the group-mean was treated as a latent variable, MSEM is recommended. Further, two ways are adopted to test multilevel moderation in the multilevel structural equation model: random coefficient prediction (RCP) for cross-level moderations, and LMS for same-level moderations. The moderation effect analysis of longitudinal data is divided into three types. The first type is moderation analysis in two-instance repeated measures designs, in which only the dependent variable is repeated measurement. In the second type, there isn’t any moderator, while both the independent and dependent variables are repeated measurement (e.g., the cross-lagged model, and the contextual moderation model). In the third type, all variables are repeated measurement, such as the latent growth model and multilevel model. Two-level regression model is recommended to analyze the moderation effect of single-level data. It can be employed to analyze the moderation effect of both observed variables and latent variables. Some international frontiers of methodological research on moderation analysis are briefly introduced: the combination of LMS and Bayesian method, moderation analysis of multiple moderators; moderation analysis of longitudinal data.

  • 预测视角下双因子模型与高阶因子模型的一般性模拟比较

    Subjects: Psychology >> Social Psychology submitted time 2023-03-27 Cooperative journals: 《心理学报》

    Abstract: Mathematically, a high-order factor model is nested within a bifactor model, and the two models are equivalent with a set of proportionality constraints of loadings. In applied studies, they are two alternative models. Using a true model with the proportional constraints to create simulation data (thus both the bifactor model and high-order factor model fitted the true model), Xu, Yu and Li (2017) studied structural coefficients based on bifactor models and high-order factor models by comparing the goodness of fit indexes and the relative bias of the structural coefficient in a simulation study. However, a bifactor model usually doesn’t satisfy the proportionality constraints, and it is very difficult to find a multidimensional construct that is well fitted by a bifactor model with the proportionality constraints. Hence their simulation results couldn’t extend to general situations.Using a true model with the proportionality constraints (thus both the bifactor model and high-order factor model fitted the true model) and a true model without the proportionality constraints (thus the bifactor model fitted the true model, whereas the high-order factor model fitted a misspecified model), this Monte Carlo study investigated structural coefficients based on bifactor models and high-order factor models for either a latent or manifest variable as the criterion. Experiment factors considered in the simulation design were: (a) the loadings on the general factor, (b) the loadings on the domain specific factors, (c) the magnitude of the structural coefficient, (d) sample size. When the true model without proportionality constraints, only factors (a), (c) and (d) were considered because the loadings on domain specific factors were fixed to different levels (0.4, 0.5, 0.6, 0.7) that assured the model does not satisfy the proportionality constraints.The main findings were as follows. (1) When the proportionality constraints were held, the high-order factor model was preferred, because it had smaller relative bias of the structural coefficient, and lower type Ⅰ error rates (but also lower statistical power, which was not a problem for a large sample). (2) When the proportionality constraints were not held, however, the bifactor model was better, because it had smaller relative bias of the structural coefficient, and higher statistical power (but also higher type Ⅰ error rates, which was not a problem for a large sample). (3) Bi-factor models fitted the simulation data better than high-order factor models in terms of fit indexes CFI, TLI, RMSEA, and SRMR whether the proportionality constraints were held or not. However, the bifactor models were less fitted according to information indexes (i.e., AIC, ABIC) when the proportionality constraints were held. (4) Whether the criterion was a manifest variable or a latent variable, the results were similar. However, for the manifest criterion variable, the relative bias of the structural coefficient was smaller.In conclusion, a high-order factor model could be the first choice to predict a criterion under the condition of proportionality constraints or well fitted for the sake of parsimony. Otherwise, a bifactor model is better for studying structural coefficients. The sample size should be large enough (e.g., 500+) no matter which model is employed.

  • 追踪研究中的内生性问题:来源与应对

    submitted time 2023-03-25 Cooperative journals: 《心理科学进展》

    Abstract: Longitudinal cross-lagged models have been widely used to analyze causal relations in behavioral and psychological sciences, and the cross-lagged panel model (CLPM) is common and important. The CLPM and related panel data models usually consist of two kinds of regression relations: (a) the autoregressive effects of a variable from its prior state (an earlier time point) to its current state (present time point) and (b) the cross-lagged effects of one variable at the prior state to another variable at the current state. These effects between the two constructs provide the foundation and crucial information in deciding on their diachronic causation. Importantly, in contrast to general regression models, a CLPM consists of a complex set of regression equations, making it more susceptible to endogeneity-related problems.Endogeneity is a critical concern in regression analyses, which refers to situations when an explanatory variable is correlated with the residual (error) of its regression equation. It will likely lead to over- or under-estimated bias with commonly used estimators. Endogeneity is a critical concern when using regression models to analyze observational data to make causal claims. The CLPM determines diachronic causation based on two kinds of regression effects (autoregressive and cross-lagged paths). Despite its vulnerability to endogeneity, this issue has received little attention and requires systematic analyses.The current study focuses on issues related to endogeneity in the CLPM. We first clarify the main sources of endogeneity problems. Then, we systematically analyze different endogeneity issues in the CLPM. Lastly, we provide an empirical example to illustrate the use of the instrumental variables (IV) method in the CLPM.IV originates from econometrics and refers to the predictor of a predictor. The IV method is probably the most popular approach while dealing with endogeneity. Researchers often incorporate suitable IVs in the model to provide unbiased estimates and alleviate the endogeneity concerns. The model implied IVs (MIIVs) have been frequently used in empirical studies. A MIIV is an IV identified within the model. The MIIVs offer a promising way to deal with endogeneity in longitudinal analyses. Typically, a MIIV is a chronologically prior observation of an exogenous variable in the model. Currently, applications with IV are underutilized in psychological research. This paper tries to illustrate the use of MIIV in the CLPM by an empirical example. To our knowledge, this is the first study to discuss endogeneity issues in the CLPM and explore the performances of MIIV in the longitudinal cross-lagged model. We find that common possible sources of endogeneity in the CLPM are: omitted variables, dynamic panel, and reciprocal relation. The omitted variables are ubiquitous in all empirical research and the omitted variable problem will affect the estimation of cross-lagged analyses. For the dynamic panel, “dynamic” refers to the use of the prior outcome as a predictor. Including the effects of this lagged outcome increases the probability of the explanatory variable being related to the residual. Besides, biases could arise from the reciprocal relation, which is also known as the feedback relation, simultaneity, or simultaneous causality. We conclude, first, there are various types of endogeneity in the CLPM, including the omitted variables, dynamic panel, and reciprocal relation. Second, endogeneity could distort the estimation of cross-lagged effects in the CLPM. Lastly, MIIV is a promising technique to tackle endogeneity issues in the CLPM. For future research, it would be interesting to explore the performance of MIIV in models extended from the CLPM. They may include the Random Intercept-CLPM, the Latent Cure Model with Structured Residuals (LCM-SR), and the Latent Change Score Model (LCS).This paper reviews the main sources of endogeneity in the CLPM to raise applied researchers' awareness of the endogeneity issues in longitudinal research. We recommend the MIIV-CLPM as a solution to deal with the endogeneity issue.

  • Exploring the longitudinal relations: Based on longitudinal models with cross-lagged structure

    Subjects: Psychology >> Statistics in Psychology submitted time 2022-08-08

    Abstract:基于交叉滞后结构的追踪模型对于揭示变量间纵向关系具有重要作用,也为因果关系的验证奠定了基础。交叉滞后面板模型在一定条件下可转换为其他形式的模型,如何选择适当的模型是重要的议题。本文对各模型进行概述,并从模型结构、预设轨迹、时间点要求等方面进行比较,最后通过一个实例说明如何选择适当的模型。结果表明,不同模型在变量关系的判断上可能给出很不同的结果,实际运用中应当有模型选择和模型比较的意识。

  • Methodological research and model development of structural equation models in China’s mainland from 2001 to 2020

    Subjects: Psychology >> Statistics in Psychology Subjects: Psychology >> Psychological Measurement submitted time 2022-03-08

    Abstract:

    In the first two decades of the twenty-first century, the hotspots of the methodological research on structural equation models (SEM) in China's mainland generally involve the following five aspects: model development, parameter estimation, model evaluation, measurement invariance and special data processing. Remarkably, there is more progress in model development (i.e., different variations of SEM) amongst the above aspects. After an overview of the background knowledge of these hotspots, we presented the main research topics and methodological achievements under each hotspot. We also discussed the recent progress of the foreign methodological studies on SEM and the future research directions.

  • Controlling for Clustering in Single Level Study: Design-Based Methods

    Subjects: Psychology >> Statistics in Psychology submitted time 2022-03-01

    Abstract:

    In social science research fields, single-level research often adopts cluster sampling or multi-stage sampling to obtain samples, resulting in the fact that the data structure is multi-level. Thus, researchers have to control for errors from the higher level in their single-level studies.

    Hierarchical linear model (HLM) suffers from limitations in dealing with such issue. First, HLM's unique advantage to focus on random effects and cluster-specific inferences cannot be reflected in single-level research. Second, the disadvantages of HLM are amplified in single-level research. (1) HLM's assumptions about random effects are harder to satisfy and test. Violation of these assumptions may result in parameter estimation bias. (2) HLM is more likely to produce convergence problems. (3) For single-level studies, HLM is complex in theory, modeling, software operation and interpretation of results. Thus, HLM is difficult to generalize in a single level study with multi-level error.

    Design-based methods (DBM), including cluster-robust standard errors (CRSE), generalized estimation equation (GEE), and fixed effects model (FEM), represent a category of logical and valid procedures to analyze multi-level data. By correcting for the standard errors of fixed effects, DBM circumvents the issues of partitioning residuals and variables into different levels while accurately estimate parameters. Thus, DBM can address multi-level data within the single-level framework, which is very friendly to single-level researchers.

    Contrast to HLM, DBM is more parsimonious in modeling, simpler in operating, more efficient in running and more robust in estimating for single-level research. Therefore, at least under the condition of single-level research with multi-level error, DBM is an ideal alternative to HLM.

    After a detailed introduction of DBM and its advantages, a simulation data set were used to demonstrate the effectiveness of DBM in controlling for multi-level error in single-level mediation studies (i.e., 1-1-1 mediation model). The results showed that although both HLM and DBM were accurate in estimating the within-cluster component of the mediating effect, the former underestimated the standard errors of mediating effect and each mediating path coefficient. In addition, all of the DBMs are simpler than HLM in terms of operations, especially the FEM. FEM is not only possible to operate through SPSS, but also unnecessary to center the variables in level 1 and control between-cluster variables. What’s more, through the popular SPSS mediating analysis macro PROCESS, FEM can realize both casual steps approach and coefficients product approach with bootstrap confidence interval for various complex mediation models.

    Finally, following suggestions were given for practitioners to select appropriate methods to accommodate clustering in single-level research. (1) DBM is suggested to control the multi-level error in single-level study, especially FEM. (2) If researchers are interested in between-cluster fixed effects, CRSE and GEE is recommended. (3) When researchers have sufficient background knowledge of HLM, and need to focus on random effects, they should collect multi-level data deliberately, especially to ensure that the sample size of level 2 is sufficient. (4) It is recommended to retain the cluster identification information when collecting data, so as to prevent the actual level of data from exceeding the expectant level, leading to the failure to control the multi-level error.

  • The second type of mediated moderation

    Subjects: Psychology >> Statistics in Psychology submitted time 2022-02-02

    Abstract:

    "Mediated moderation is frequently used in psychological research to reveal the phenomenon of a moderating effect being indirectly realized through mediating variables. This paper introduces the concept and advantages of a second type of mediated moderation (meMO-II). Then, we compare meMO-II with other models that combine mediation and moderation. Additionally, we propose the meMO-II modeling approach and analysis process, which we then demonstrated with a real example. We also introduce meMO-II analysis methods based on latent variables, advances in meMO-II modeling approaches, and variations in meMO-II. This offers a valuable contribution to moderating mechanism research.

  • 基于两水平回归模型的调节效应分析及其效应量

    Subjects: Psychology >> Statistics in Psychology submitted time 2021-12-09

    Abstract:使用多元回归法进行调节效应分析在社科领域已常有应用。简述了目前多元回归法的调节效应分析存在的不足,包括人为变换检验模型、自变量和调节变量区分不足、误差方差齐性的假设难以满足、调节效应量指标△R2没有直接测量调节变量对自变量与因变量关系的调节程度。比较好的方法是用两水平回归模型进行调节效应分析并使用相应的效应量指标。在介绍新方法和新效应量后,总结出一套调节效应的分析流程,通过一个例子来演示如何用Mplus软件进行两水平回归模型的调节效应及其效应量分析。最后讨论了两水平回归模型的调节效应分析的发展,包括稳健的调节效应分析、潜变量的调节效应分析、有调节的中介效应分析和有中介的调节效应分析等。

  • Standardized Estimates for Latent Interaction Effects: Method Comparison and Selection Strategy

    Subjects: Psychology >> Statistics in Psychology submitted time 2021-10-12

    Abstract: Analyzing the interaction effect of latent variables has become an important topic in both theoretical and empirical studies. Standardized estimation plays an important role in model interpretation and effect comparison. Although Wen et al. (2010) has formulated the appropriate standardized estimation for the latent interaction effects, there is no popular commercial software that provides the appropriate standardized estimation before the launch of Mplus 8.2 in 2019. Previous comparisons of methods for estimating latent interaction were based on the original estimation. In this study, through a simulation experiment, the appropriate standardized estimation of latent interaction effects is obtained respectively by four methods: the product indicator (PI) approach, Latent Moderated Structural Equations (LMS), Bayesian method without prior information (BN), and Bayesian method with prior information (BI). Then these estimations are compared in terms of the bias of estimation, the bias of standard error, type Ⅰ error rate and statistical power. The true model in the simulation is based on the structural equation η=0.4ξ_1+0.4ξ_2+γ_3 ξ_1 ξ_2+ζ where the latent variables η, ξ_1, ξ_2 each had three indicators with a standardized factor loading of 0.7. Experiment factors include the distribution of two exogenous latent variables (normal, non-normal), correlation ϕ_12 between two exogenous latent variables (0, 0.3 and 0.7), interaction effect γ_3 (0, 0.2), sample size N (100, 200, and 500) and estimation method (PI, LMS, BN, BI). There are five main findings. (1) the proportion of proper solution of LMS and the two Bayesian methods were close to 100% in all treatments, while PI was almost fully proper when N = 500. (2) Under the normal condition, the bias of standardized estimation of latent interaction obtained by LMS, BI and BN was ignorable, and PI was acceptable when N = 500. Under the non-normal condition, the bias of LMS and Bayesian methods inflated seriously with increasing correlation of two exogenous latent variables, but PI was still acceptable when N = 500. (3) Under both distribution conditions, the bias of standard error of standardized estimation of latent interaction obtained by LMS and BN was small and acceptable, while PI was acceptable when N = 500, and BI tended to overestimate the standard error. (4) Under normal conditions, the type I error rates of LMS were acceptable only when the sample size was large, while the other methods were acceptable in all conditions. Under the non-normal condition, the type I error rates of PI were still acceptable, while the other methods were acceptable only when the sample size was small or the correlation between two exogenous latent variables was low. (5) The statistical power of latent interaction obtained by PI was lower than that by any other method, and a large sample size (e.g., N=500) was required to ensure the PI with statistical power over 80%; LMS and BN had higher statistical power, while BI had the highest one in all conditions. For the latent interaction, the results of comparing different methods in standardized estimation are quite similar to those in the original estimation. Under the normal condition, it is recommended to use LMS to estimate the interaction effect of latent variables, with the caution of Type I error rate and effect size for inference. If accurate prior information can be obtained, Bayesian method is preferred, especially in the case of a small sample. When the variables are not normally distributed, the unconstrained product indicator approach is recommended, which is more robust than the other methods, but the sample size should be large enough (N =500 or above). If the correlation between exogenous latent variables is low (it can be estimated and tested by confirmatory factor analysis), Bayesian method without prior information can be considered for small samples.