The Analysis of Multivariate Longitudinal Data: An Instructive Application of the Longitudinal Three-Mode Model

Measurement invariance in the social sciences: Historical development, methodological challenges, state of the art, and future perspectives

This review summarizes the current state of the art of statistical and (survey) methodological research on measurement (non)invariance, which is considered a core challenge for the comparative social sciences. After outlining the historical roots, conceptual details, and standard procedures for measurement invariance testing, the paper focuses in particular on the statistical developments that have been achieved in the last 10 years. These include Bayesian approximate measurement invariance, the alignment method, measurement invariance testing within the multilevel modeling framework, mixture multigroup factor analysis, the measurement invariance explorer, and the response shift-true change decomposition approach. Furthermore, the contribution of survey methodological research to the construction of invariant measurement instruments is explicitly addressed and highlighted, including the issues of design decisions, pretesting, scale adoption, and translation. The paper ends with an outlook on future research perspectives.

Multivariate linear mixed models with censored and nonignorable missing outcomes, with application to AIDS studies

The analysis of multivariate longitudinal data could encounter some complications due to censorship induced by detection limits of the assay and nonresponse occurring when participants missed scheduled visits intermittently or discontinued participation. This paper establishes a generalization of the multivariate linear mixed model that can accommodate censored responses and nonignorable missing outcomes simultaneously. To account for the nonignorable missingness, the selection approach which decomposes the joint distribution as a marginal distribution for the primary outcome variables and a model describing the missing process conditional on the hypothetical complete data is used. A computationally feasible Monte Carlo expectation conditional maximization algorithm is developed for parameter estimation with the maximum likelihood (ML) method. Furthermore, a general information-based approach is presented to assess the variability of ML estimators. The techniques for the prediction of censored responses and imputation of missing outcomes are also discussed. The methodology is motivated and exemplified by a real dataset concerning HIV-AIDS clinical trials. A simulation study is conducted to examine the performance of the proposed method compared with other traditional approaches.

Parsimonious hidden Markov models for matrix-variate longitudinal data

Hidden Markov models (HMMs) have been extensively used in the univariate and multivariate literature. However, there has been an increased interest in the analysis of matrix-variate data over the recent years. In this manuscript we introduce HMMs for matrix-variate balanced longitudinal data, by assuming a matrix normal distribution in each hidden state. Such data are arranged in a four-way array. To address for possible overparameterization issues, we consider the eigen decomposition of the covariance matrices, leading to a total of 98 HMMs. An expectation-conditional maximization algorithm is discussed for parameter estimation. The proposed models are firstly investigated on simulated data, in terms of parameter recovery, computational times and model selection. Then, they are fitted to a four-way real data set concerning the unemployment rates of the Italian provinces, evaluated by gender and age classes, over the last 16 years.

Investigation of measurement invariance in longitudinal health-related quality of life in preemptive or previously dialyzed kidney transplant recipients

PURPOSE

Kidney transplantation (KT) can impact patients' evaluation of health-related quality of life (HRQoL) as they adapt to their new life with a graft and its changes. Patients may adapt to KT in a different way, depending on whether they were on dialysis prior to transplantation or not (i.e. preemptive group). This may result in lack of measurement invariance between these patients' groups and/or over time (i.e. response shift, RS) which may invalidate the between-group comparison of HRQoL change scores. The aim of this study was to investigate and compare RS before and after KT between these two patients' groups. Measurement invariance was investigated between groups and over time with three measurement occasions.

METHODS

Adult patients completed the SF-36 at the last visit before KT, and 3, 6 months after. A structural equation model-based procedure was used to (i) detect and take into account measurement non-invariance between groups and RS, if appropriate, (ii) identify the period of occurrence of RS, (iii) study the heterogeneity of RS between the two groups.

RESULTS

Before KT (i.e. baseline), measurement invariance was not rejected between dialyzed (n = 196) and preemptive (n = 178) patients' groups. Between baseline and 3 months after KT, similar uniform recalibration was detected on the general health domain in both groups. Uniform recalibration was found between 3- and 6 months after KT on the vitality domain for preemptive patients only.

CONCLUSION

HRQoL, adjusted for RS, increased overall for preemptive and dialyzed kidney transplant patients after transplantation. RS may reflect differing adaptation processes following KT.

Critical examination of current response shift methods and proposal for advancing new methods

Purpose

This work is part of an international, interdisciplinary initiative to synthesize research on response shift in results of patient-reported outcome measures. The objective is to critically examine current response shift methods. We additionally propose advancing new methods that address the limitations of extant methods.

Methods

Based on literature reviews, this critical examination comprises design-based, qualitative, individualized, and preference-based methods, latent variable models, and other statistical methods. We critically appraised their definition, operationalization, the type of response shift they can detect, whether they can adjust for and explain response shift, their assumptions, and alternative explanations. Overall limitations requiring new methods were identified.

Results

We examined 11 methods that aim to operationalize response shift, by assessing change in the meaning of one’s self-evaluation. Six of these methods distinguish between change in observed measurements (observed change) and change in the construct that was intended to be measured (target change). The methods use either (sub)group-based or individual-level analysis, or a combination. All methods have underlying assumptions to be met and alternative explanations for the inferred response shift effects. We highlighted the need to address the interpretation of the results as response shift and proposed advancing new methods handling individual variation in change over time and multiple time points.

Conclusion

No single response shift method is optimal; each method has strengths and limitations. Additionally, extra steps need to be taken to correctly interpret the results. Advancing new methods and conducting computer simulation studies that compare methods are recommended to move response shift research forward.

Supplementary Information

The online version of this article (10.1007/s11136-020-02755-4) contains supplementary material, which is available to authorized users.

Using structural equation modeling to investigate change and response shift in patient-reported outcomes: practical considerations and recommendations

BACKGROUND

Patient-reported outcomes (PROs) are of increasing importance for health-care evaluations. However, the interpretation of change in PROs may be obfuscated due to changes in the meaning of the self-evaluation, i.e., response shift. Structural equation modeling (SEM) is the most widely used statistical approach for the investigation of response shift. Yet, non-technical descriptions of SEM for response shift investigation are lacking. Moreover, application of SEM is not straightforward and requires sequential decision-making practices that have not received much attention in the literature.

AIMS

To stimulate appropriate applications and interpretations of SEM for the investigation of response shift, the current paper aims to (1) provide an accessible description of the SEM operationalizations of change that are relevant for response shift investigation; (2) discuss practical considerations in applying SEM; and (3) provide guidelines and recommendations for researchers who want to use SEM for the investigation and interpretation of change and response shift in PROs.

CONCLUSION

Appropriate applications and interpretations of SEM for the detection of response shift will help to improve our understanding of response shift phenomena and thus change in PROs. Better understanding of patients' perceived health trajectories will ultimately help to adopt more effective treatments and thus enhance patients' wellbeing.