Equidistant Response Options on Likert-Type Instruments: Testing the Interval Scaling Assumption Using Mplus

The purpose of the present study was to provide the means to evaluate the "interval-scaling" assumption that governs the use of parametric statistics and continuous data estimators in self-report instruments that utilize Likert-type scaling. Using simulated and real data, the methodology to test for this important assumption is evaluated using the popular software Mplus 8.8. Evidence on meeting the assumption is provided using the Wald test and the equidistant index. It is suggested that routine evaluations of self-report instruments engage the present methodology so that the most appropriate estimator will be implemented when testing the construct validity of self-report instruments.

The item position effects in international examinations: the roles of gender

The goal of the present study was to evaluate the roles of item position in terms of item difficulty levels in the assessment of aptitude. Using data from a National Examination in Saudi Arabia, the item position effect was evaluated as a teacher licensure test (GTLT) was administered using five different forms with the same items appearing in a different order. Results indicated minuscule in magnitude position effects estimates, overall, with initially 11.1% of the tests being significant but all of them failing to reach significance using the Holm-Bonferroni's and Sidak corrective procedures. With regard to gender, item position effects emerged in 47.6% of the tests after adjusting the level of significance using the Sidak correction. Interestingly, the direction of effect was consistent so that in 87% of the significant gender comparisons, item position effects were in the direction where females were spending more time on items when they appeared in later positions on the test compared to males. Assuming that items appearing later on the test are likely more difficult, the present findings suggest a profile of deep processing and active engagement in females when facing achievement tests.

Exploratory structural equation modeling: a streamlined step by step approach using the R Project software

Confirmatory Factor Analysis (CFA) has been a popular yet limited approach to assessing latent factor structures. Despite items rarely loading exclusively on one latent factor in multifactorial scales, CFA assumes all indicators/items should load uniquely on their allocated latent dimensions. To address this weakness, Exploratory Structural Equation Modeling (ESEM) combines exploratory factor analyses (EFA) and CFA procedures, allowing cross-loadings to occur when assessing hypothesized models. Although such advantages have enhanced ESEM popularity, its adoption is often limited by software rigidity and complex coding difficulties. To address these obstacles, the current tutorial presents a streamlined, step-by-step approach using the open-source software R while providing both R and Mplus ESEM syntax. The tutorial demonstrates the sequence of the ESEM stages by examining the frequently debated Strengths and Difficulties Questionnaire (SDQ) factor structure, using openly accessible data from the Longitudinal Study of Australian Children (LSAC). As ESEM may allow a better understanding of the complex associations in multidimensional scales, this tutorial may optimize the epidemiological and clinical assessment of common yet multifaceted psychiatric presentations.

The dynamic interplay between sleep and mood: an intensive longitudinal study of individuals with bipolar disorder

BACKGROUND

Sleep disturbances are important symptoms to monitor in people with bipolar disorder (BD) but the precise longitudinal relationships between sleep and mood remain unclear. We aimed to examine associations between stable and dynamic aspects of sleep and mood in people with BD, and assess individual differences in the strength of these associations.

METHODS

Participants (N = 649) with BD-I (N = 400) and BD-II (N = 249) provided weekly self-reports of insomnia, depression and (hypo)mania symptoms using the True Colours online monitoring tool for 21 months. Dynamic structural equation models were used to examine the interplay between weekly reports of insomnia and mood. The effects of clinical and demographic characteristics on associations were also assessed.

RESULTS

Increased variability in insomnia symptoms was associated with increased mood variability. In the sample as a whole, we found strong evidence of bidirectional relationships between insomnia and depressive symptoms but only weak support for bidirectional relationships between insomnia and (hypo)manic symptoms. We found substantial variability between participants in the strength of prospective associations between insomnia and mood, which depended on age, gender, bipolar subtype, and a history of rapid cycling.

CONCLUSIONS

Our results highlight the importance of monitoring sleep in people with BD. However, researchers and clinicians investigating the association between sleep and mood should consider subgroup differences in this relationship. Advances in digital technology mean that intensive longitudinal data on sleep and mood are becoming increasingly available. Novel methods to analyse these data present an exciting opportunity for furthering our understanding of BD.

Identifying Ability and Nonability Groups: Incorporating Response Times Using Mixture Modeling

The goal of the present study was to address the analytical complexity of incorporating responses and response times through applying the Jeon and De Boeck mixture item response theory model in Mplus 8.7. Using both simulated and real data, we attempt to identify subgroups of responders that are rapid guessers or engage knowledge retrieval strategies. When applying the mixture model to a measure of contextual error in linguistics results pointed to the presence of a knowledge retrieval strategy. That is, a participant either knows the content (morphology, grammar rules) and can identify the error, or lacks the requisite knowledge and cannot benefit from spending more time on an item. In contrast, as item difficulty progressed, the high-ability group utilized the additional time to make informed guesses. The methodology is illustrated using annotated code in Mplus 8.7.

Required sample size to detect mediation in 3-level implementation studies

Background

Statistical tests of mediation are important for advancing implementation science; however, little research has examined the sample sizes needed to detect mediation in 3-level designs (e.g., organization, provider, patient) that are common in implementation research. Using a generalizable Monte Carlo simulation method, this paper examines the sample sizes required to detect mediation in 3-level designs under a range of conditions plausible for implementation studies.

Method

Statistical power was estimated for 17,496 3-level mediation designs in which the independent variable (X) resided at the highest cluster level (e.g., organization), the mediator (M) resided at the intermediate nested level (e.g., provider), and the outcome (Y) resided at the lowest nested level (e.g., patient). Designs varied by sample size per level, intraclass correlation coefficients of M and Y, effect sizes of the two paths constituting the indirect (mediation) effect (i.e., X→M and M→Y), and size of the direct effect. Power estimates were generated for all designs using two statistical models—conventional linear multilevel modeling of manifest variables (MVM) and multilevel structural equation modeling (MSEM)—for both 1- and 2-sided hypothesis tests.

Results

For 2-sided tests, statistical power to detect mediation was sufficient (≥0.8) in only 463 designs (2.6%) estimated using MVM and 228 designs (1.3%) estimated using MSEM; the minimum number of highest-level units needed to achieve adequate power was 40; the minimum total sample size was 900 observations. For 1-sided tests, 808 designs (4.6%) estimated using MVM and 369 designs (2.1%) estimated using MSEM had adequate power; the minimum number of highest-level units was 20; the minimum total sample was 600. At least one large effect size for either the X→M or M→Y path was necessary to achieve adequate power across all conditions.

Conclusions

While our analysis has important limitations, results suggest many of the 3-level mediation designs that can realistically be conducted in implementation research lack statistical power to detect mediation of highest-level independent variables unless effect sizes are large and 40 or more highest-level units are enrolled. We suggest strategies to increase statistical power for multilevel mediation designs and innovations to improve the feasibility of mediation tests in implementation research.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13012-022-01235-2.

Changes in Relationship Commitment Across the Transition to Parenthood: Pre-pregnancy Happiness as a Protective Resource

The transition to parenthood is both a joyous and a challenging event in a relationship. Studies to date have found mostly negative effects of the birth of the first child on the parental relationship. We propose that partners' pre-pregnancy individual happiness may serve as a buffer against these negative effects. We predicted that parents who are happy prior to pregnancy fare better in terms of relationship commitment after childbirth than unhappy parents. To test our prediction, we used data of a 5-wave longitudinal study among 109 Dutch newlywed couples who had their first child during the study and a comparison group of 55 couples who remained childless. We found that the relationship commitment of fathers with higher pre-pregnancy happiness and fathers with a partner with higher pre-pregnancy happiness increased slightly in the years after childbirth, whereas the relationship commitment of fathers with lower pre-pregnancy happiness and fathers with a partner with lower pre-pregnancy happiness decreased. In addition, the relationship commitment of mothers with a happier partner prior to pregnancy decreased only slightly across the transition to parenthood but showed a steeper decline for mothers with a partner with average or lower pre-pregnancy happiness. In line with the idea that happiness acts as a resource when partners have to deal with relationship challenges, individual happiness predicted changes in relationship commitment for parents, but not for partners who remained childless.

Comparing multiple statistical software for multiple-indicator, multiple-cause modeling: an application of gender disparity in adult cognitive functioning using MIDUS II dataset

BACKGROUND

The multiple-indicator, multiple-cause model (MIMIC) incorporates covariates of interest in the factor analysis. It is a special case of structural equation modeling (SEM), which is modeled under latent variable framework. The MIMIC model provides rigorous results and becomes broadly available in multiple statistical software. The current study introduces the MIMIC model and how it can be implemented using statistical software packages SAS CALIS procedure, R lavaan package, and Mplus version 8.0.

METHODS

In this paper, we first discussed the formulation of the MIMIC model with regard to model specification and identification. We then demonstrated the empirical application of the MIMIC model with the Midlife in the United States II (MIDUS II) Study (N = 4109) using SAS CALIS procedure, R lavaan package and Mplus version 8.0 to examine gender disparities in cognitive functioning. The input, output, and diagram syntaxes of the three statistical software packages were also presented.

RESULTS

In terms of data structure, all three statistical programs can be conducted using both raw data and empirical covariance matrix. SAS and R are comprehensive statistical analytic packages and encompass numerous data manipulation capacities. Mplus is designed primarily for latent variable modeling and has far more modeling flexibility compared to SAS and R, but limited in data manipulation. Differences in model results from the three statistical programs are trivial. Overall, the results show that while men show better performance in executive function than women, women demonstrate better episodic memory than men.

CONCLUSIONS

Our study demonstrates the utility of the MIMIC model in its empirical application, fitted with three popular statistical software packages. Results from our models align with empirical findings from previous research. We provide coding procedures and examples with detailed explanations in the hopes of providing a concise tutorial for researchers and methodologists interested in incorporating latent constructs with multiple indicators and multiple covariates in their research projects. Future researchers are encouraged to adopt this flexible and rigorous modeling approach.

On the Statistical and Practical Limitations of Thurstonian IRT Models

Forced-choice questionnaires have been proposed to avoid common response biases typically associated with rating scale questionnaires. To overcome ipsativity issues of trait scores obtained from classical scoring approaches of forced-choice items, advanced methods from item response theory (IRT) such as the Thurstonian IRT model have been proposed. For convenient model specification, we introduce the thurstonianIRT R package, which uses Mplus, lavaan, and Stan for model estimation. Based on practical considerations, we establish that items within one block need to be equally keyed to achieve similar social desirability, which is essential for creating forced-choice questionnaires that have the potential to resist faking intentions. According to extensive simulations, measuring up to five traits using blocks of only equally keyed items does not yield sufficiently accurate trait scores and inter-trait correlation estimates, neither for frequentist nor for Bayesian estimation methods. As a result, persons' trait scores remain partially ipsative and, thus, do not allow for valid comparisons between persons. However, we demonstrate that trait scores based on only equally keyed blocks can be improved substantially by measuring a sizable number of traits. More specifically, in our simulations of 30 traits, scores based on only equally keyed blocks were non-ipsative and highly accurate. We conclude that in high-stakes situations where persons are motivated to give fake answers, Thurstonian IRT models should only be applied to tests measuring a sizable number of traits.

Estimation of an IRT Model by Mplus for Dichotomously Scored Responses Under Different Estimation Methods

The purpose of this article is twofold. The first is to provide evaluative information on the recovery of model parameters and their standard errors for the two-parameter item response theory (IRT) model using different estimation methods by Mplus. The second is to provide easily accessible information for practitioners, instructors, and students about the relationships between IRT and item factor analysis (FA) parameterizations. Specifically, this is done using the "Theta" and "Delta" parameterizations in Mplus for unidimensional and multidimensional modeling with dichotomous and polytomous responses with and without the scaling constant D. The first objective aims at investigating differences that may occur when using different estimation methods in Mplus for binary response modeling. The second objective was motivated by practical interest observed among graduate students and applied researchers. The relations between IRT and Mplus FA "Theta" and "Delta" parameterizations are described using expressions without the use of matrices, which can be understood efficiently by applied researchers and students.

Using iMCFA to Perform the CFA, Multilevel CFA, and Maximum Model for Analyzing Complex Survey Data

To construct CFA, MCFA, and maximum MCFA with LISREL v.8 and below, we provide iMCFA (integrated Multilevel Confirmatory Analysis) to examine the potential multilevel factorial structure in the complex survey data. Modeling multilevel structure for complex survey data is complicated because building a multilevel model is not an infallible statistical strategy unless the hypothesized model is close to the real data structure. Methodologists have suggested using different modeling techniques to investigate potential multilevel structure of survey data. Using iMCFA, researchers can visually set the between- and within-level factorial structure to fit MCFA, CFA and/or MAX MCFA models for complex survey data. iMCFA can then yield between- and within-level variance-covariance matrices, calculate intraclass correlations, perform the analyses and generate the outputs for respective models. The summary of the analytical outputs from LISREL is gathered and tabulated for further model comparison and interpretation. iMCFA also provides LISREL syntax of different models for researchers' future use. An empirical and a simulated multilevel dataset with complex and simple structures in the within or between level was used to illustrate the usability and the effectiveness of the iMCFA procedure on analyzing complex survey data. The analytic results of iMCFA using Muthen's limited information estimator were compared with those of Mplus using Full Information Maximum Likelihood regarding the effectiveness of different estimation methods.

MplusAutomation: An R Package for Facilitating Large-Scale Latent Variable Analyses in Mplus

MplusAutomation is a package for R that facilitates complex latent variable analyses in Mplus involving comparisons among many models and parameters. More specifically, MplusAutomation provides tools to accomplish three objectives: to create and manage Mplus syntax for groups of related models; to automate the estimation of many models; and to extract, aggregate, and compare fit statistics, parameter estimates, and ancillary model outputs. We provide an introduction to the package using applied examples including a large-scale simulation study. By reducing the effort required for large-scale studies, a broad goal of MplusAutomation is to support methodological developments in structural equation modeling using Mplus.

[The latent variable growth curve model of longitudinal data and its implementation in Mplus]

To discuss the latent variable growth curve model of longitudinal data and give its implementation method in Mplus. The application of Mplus software has been used to deal with the longitudinal data of mental health status of college students in an university. Results show that the model can process the longitudinal data with latent variables, which can compare the differences of the overall development trend and individual development, also taking a covariate into the model to improve the effect of model fitting. Using Mplus software to process the longitudinal data with latent variables, the program is simple and easy to operate. This study provides the latent variable growth curve model of longitudinal data and its procedure of implementation in Mplus, and the statistical methodology guidance and reference for practical applications of epidemiological cohort study.

Introduction to bifactor polytomous item response theory analysis

A bifactor item response theory model can be used to aid in the interpretation of the dimensionality of a multifaceted questionnaire that assumes continuous latent variables underlying the propensity to respond to items. This model can be used to describe the locations of people on a general continuous latent variable as well as on continuous orthogonal specific traits that characterize responses to groups of items. The bifactor graded response (bifac-GR) model is presented in contrast to a correlated traits (or multidimensional GR model) and unidimensional GR model. Bifac-GR model specification, assumptions, estimation, and interpretation are demonstrated with a reanalysis of data (Campbell, 2008) on the Shared Activities Questionnaire. We also show the importance of marginalizing the slopes for interpretation purposes and we extend the concept to the interpretation of the information function. To go along with the illustrative example analyses, we have made available supplementary files that include command file (syntax) examples and outputs from flexMIRT, IRTPRO, R, Mplus, and STATA. Supplementary data to this article can be found online at http://dx.doi.org/10.1016/j.jsp.2016.11.001. Data needed to reproduce analyses in this article are available as supplemental materials (online only) in the Appendix of this article.

The Reduced RUM as a Logit Model: Parameterization and Constraints

Cognitive diagnosis models (CDMs) for educational assessment are constrained latent class models. Examinees are assigned to classes of intellectual proficiency defined in terms of cognitive skills called attributes, which an examinee may or may not have mastered. The Reduced Reparameterized Unified Model (Reduced RUM) has received considerable attention among psychometricians. Markov Chain Monte Carlo (MCMC) or Expectation Maximization (EM) are typically used for estimating the Reduced RUM. Commercial implementations of the EM algorithm are available in the latent class analysis (LCA) routines of Latent GOLD and Mplus, for example. Fitting the Reduced RUM with an LCA routine requires that it be reparameterized as a logit model, with constraints imposed on the parameters. For models involving two attributes, these have been worked out. However, for models involving more than two attributes, the parameterization and the constraints are nontrivial and currently unknown. In this article, the general parameterization of the Reduced RUM as a logit model involving any number of attributes and the associated parameter constraints are derived. As a practical illustration, the LCA routine in Mplus is used for fitting the Reduced RUM to two synthetic data sets and to a real-world data set; for comparison, the results obtained by using the MCMC implementation in OpenBUGS are also provided.

Error induced by the estimation of the corneal power and the effective lens position with a rotationally asymmetric refractive multifocal intraocular lens

AIM

To evaluate the prediction error in intraocular lens (IOL) power calculation for a rotationally asymmetric refractive multifocal IOL and the impact on this error of the optimization of the keratometric estimation of the corneal power and the prediction of the effective lens position (ELP).

METHODS

Retrospective study including a total of 25 eyes of 13 patients (age, 50 to 83y) with previous cataract surgery with implantation of the Lentis Mplus LS-312 IOL (Oculentis GmbH, Germany). In all cases, an adjusted IOL power (PIOLadj) was calculated based on Gaussian optics using a variable keratometric index value (nkadj) for the estimation of the corneal power (Pkadj) and on a new value for ELP (ELPadj) obtained by multiple regression analysis. This PIOLadj was compared with the IOL power implanted (PIOLReal) and the value proposed by three conventional formulas (Haigis, Hoffer Q and Holladay I).

RESULTS

PIOLReal was not significantly different than PIOLadj and Holladay IOL power (P>0.05). In the Bland and Altman analysis, PIOLadj showed lower mean difference (-0.07 D) and limits of agreement (of 1.47 and -1.61 D) when compared to PIOLReal than the IOL power value obtained with the Holladay formula. Furthermore, ELPadj was significantly lower than ELP calculated with other conventional formulas (P<0.01) and was found to be dependent on axial length, anterior chamber depth and Pkadj.

CONCLUSION

Refractive outcomes after cataract surgery with implantation of the multifocal IOL Lentis Mplus LS-312 can be optimized by minimizing the keratometric error and by estimating ELP using a mathematical expression dependent on anatomical factors.

Item response theory for measurement validity

Item response theory (IRT) is an important method of assessing the validity of measurement scales that is underutilized in the field of psychiatry. IRT describes the relationship between a latent trait (e.g., the construct that the scale proposes to assess), the properties of the items in the scale, and respondents’ answers to the individual items. This paper introduces the basic premise, assumptions, and methods of IRT. To help explain these concepts we generate a hypothetical scale using three items from a modified, binary (yes/no) response version of the Center for Epidemiological Studies-Depression scale that was administered to 19,399 respondents. We first conducted a factor analysis to confirm the unidimensionality of the three items and then proceeded with Mplus software to construct the 2-Parameter Logic (2-PL) IRT model of the data, a method which allows for estimates of both item discrimination and item difficulty. The utility of this information both for clinical purposes and for scale construction purposes is discussed.

Facing off with Scylla and Charybdis: a comparison of scalar, partial, and the novel possibility of approximate measurement invariance

Measurement invariance (MI) is a pre-requisite for comparing latent variable scores across groups. The current paper introduces the concept of approximate MI building on the work of Muthén and Asparouhov and their application of Bayesian Structural Equation Modeling (BSEM) in the software Mplus. They showed that with BSEM exact zeros constraints can be replaced with approximate zeros to allow for minimal steps away from strict MI, still yielding a well-fitting model. This new opportunity enables researchers to make explicit trade-offs between the degree of MI on the one hand, and the degree of model fit on the other. Throughout the paper we discuss the topic of approximate MI, followed by an empirical illustration where the test for MI fails, but where allowing for approximate MI results in a well-fitting model. Using simulated data, we investigate in which situations approximate MI can be applied and when it leads to unbiased results. Both our empirical illustration and the simulation study show approximate MI outperforms full or partial MI In detecting/recovering the true latent mean difference when there are (many) small differences in the intercepts and factor loadings across groups. In the discussion we provide a step-by-step guide in which situation what type of MI is preferred. Our paper provides a first step in the new research area of (partial) approximate MI and shows that it can be a good alternative when strict MI leads to a badly fitting model and when partial MI cannot be applied.

Bayesian Evaluation of inequality-constrained Hypotheses in SEM Models using Mplus

Researchers in the behavioural and social sciences often have expectations that can be expressed in the form of inequality constraints among the parameters of a structural equation model resulting in an informative hypothesis. The question they would like an answer to is "Is the Hypothesis Correct" or "Is the hypothesis incorrect?". We demonstrate a Bayesian approach to compare an inequality-constrained hypothesis with its complement in an SEM framework. The method is introduced and its utility is illustrated by means of an example. Furthermore, the influence of the specification of the prior distribution is examined. Finally, it is shown how the approach proposed can be implemented using Mplus.

POWER ANALYSIS FOR COMPLEX MEDIATIONAL DESIGNS USING MONTE CARLO METHODS

Applied researchers often include mediation effects in applications of advanced methods such as latent variable models and linear growth curve models. Guidance on how to estimate statistical power to detect mediation for these models has not yet been addressed in the literature. We describe a general framework for power analyses for complex mediational models. The approach is based on the well known technique of generating a large number of samples in a Monte Carlo study, and estimating power as the percentage of cases in which an estimate of interest is significantly different from zero. Examples of power calculation for commonly used mediational models are provided. Power analyses for the single mediator, multiple mediators, three-path mediation, mediation with latent variables, moderated mediation, and mediation in longitudinal designs are described. Annotated sample syntax for Mplus is appended and tabled values of required sample sizes are shown for some models.