Mover-stayer Model Research Articles

NURSING HOMES’ FIVE-STAR QUALITY RATING SYSTEM: FORECASTING THE FUTURE STABILITY AND VOLATILITY

Abstract The utilization of publicly reported quality measures such as nursing homes’ five-star quality rating system to hold providers accountable for their quality of care has increased over the years. Therefore, nursing homes have invested significant resources into maintaining or improving the ratings awarded to them by CMS. This study utilizes statistical models to analyze the past rating histories to predict future evolution of ratings of nursing homes. Data on all U.S. nursing homes for the years 2017 - 2021 was derived from CMS Nursing Home Compare. Primary variable represents the overall five-star quality rating of nursing homes. A Markov chain model and a Mover Stayer model are used to predict changes in ratings of nursing homes. The one-year rating transition probabilities are estimated using maximum likelihood estimation. The key findings indicate the likelihoods of future upgrades and downgrades in nursing homes’ ratings. Nursing home administrators are under constant pressure to strategically allocate resources for maintaining or improving the five-star ratings awarded to them by CMS. The findings of this study could help nursing home administrators in forecasting future change in their rating and making better resource allocation decisions such as those related to preventing a rating downgrade. The study findings could also be used by policymakers to focus on nursing homes facing downgrades and assisting them in improving their quality of service based on the potential change in their rating. The same results could also be utilized to assess the stability of ratings given to nursing homes.

Absolute and relative risk estimation in the presence ofoutcome ascertainment gaps and competing risks.

Incomplete coverage by cancer registries can lead to an underreporting of cancers and a resulting bias in risk estimates. When registries are defined by geographic region, gaps in observation can arise for individuals who reside outside of or migrate from the total registry catchment area. Moreover, the exact periods of non-observation for an individual may be unknown due to intermittent reporting of residential histories. The motivating example for this work is the U.S. Radiologic Technologist (USRT) study which ascertained cancer outcomes for a national cohort through 43 state/regional registries; similar gaps in outcome ascertainment can appear in other registry or electronic health record- based cohort studies. We propose a two-step procedure for estimating relative and absolute risk in these settings. First, using a mover stayer model fitted to individuals' known residential history, we obtain individual posterior probabilities of residing outside the registry catchment area each year. Second, we incorporate these probabilities in the survival data likelihood for competing risks to account for unobserved events. We assess the performance of the proposed method in extensive simulation studies. Compared to several simple alternative approaches, the proposed method reduces bias and improves efficiency. Finally, we apply the proposed method to a study of first primary lung cancers in the USRT cohort.

An imputation approach for a time-to-event analysis subject to missing outcomes due to noncoverage in disease registries.

Disease incidence data in a national-based cohort study would ideally be obtained through a national disease registry. Unfortunately, no such registry currently exists in the United States. Instead, the results from individual state registries need to be combined to ascertain certain disease diagnoses in the United States. The National Cancer Institute has initiated a program to assemble all state registries to provide a complete assessment of all cancers in the United States. Unfortunately, not all registries have agreed to participate. In this article, we develop an imputation-based approach that uses self-reported cancer diagnosis from longitudinally collected questionnaires to impute cancer incidence not covered by the combined registry. We propose a two-step procedure, where in the first step a mover-stayer model is used to impute a participant's registry coverage status when it is only reported at the time of the questionnaires given at 10-year intervals and the time of the last-alive vital status and death. In the second step, we propose a semiparametric working model, fit using an imputed coverage area sample identified from the mover-stayer model, to impute registry-based survival outcomes for participants in areas not covered by the registry. The simulation studies show the approach performs well as compared with alternative ad hoc approaches for dealing with this problem. We illustrate the methodology with an analysis that links the United States Radiologic Technologists study cohort with the combined registry that includes 32 of the 50 states.

Examining the multidimensional energy poverty trap and its determinants: An empirical analysis at household and community levels in six provinces of China

Modern energy services that are close to perfect are the basis for sustainable development. Measuring energy poverty from a multidimensional perspective and revealing its dynamic evolution has important practical significance for formulating and improving energy policies. After measuring the multidimensional energy poverty index of China's six provinces using data from 2009, 2011, and 2015, this study divided households into three states: non-multidimensional energy poverty, multidimensional energy poverty, and severe multidimensional energy poverty. The stay proportion and migration probability of households in different states were estimated by the mover-stayer model, and their determinants were analyzed at the household and community levels by the hierarchical linear model. The results show that the multidimensional energy poverty of China's six provinces declined. Most households migrated to better states, which indicates that there is no energy poverty trap in China. However, there are risks of returning to poverty in some households. For stayers, the change of their status is formed by the joint action of the household and community, whereas for the movers, it is mainly due to the household conditions. We suggest that, according to the different levels of energy poverty, energy policies should be formulated at different levels and stages.

A new framework for examining creditworthiness of borrowers: the mover-stayer model with covariate and macroeconomic effects

We develop a novel extension of the mover-stayer model to allow for time-dependent variables such as macroeconomic factors and apply it to the repayment process for car loans. The MS model postulates a simple form of population heterogeneity, which is particularly well suited to describing the repayment process: a proportion of borrowers always repay on time (stayers), and a complementary proportion evolves according to a discrete-time Markov chain (movers), with an absorbing default state. In contrast to the literatures focus on the determinants of defaults, our extension examines the determinants of creditworthy borrowers (stayers). We model the probability of borrowers being stayers as a logistic function of their time-fixed covariates as well as of macroeconomic variables. The car-loans data set, obtained from a Polish bank, contains a large number of characteristics for each borrower and their repayment histories. The MS models' estimation from these data indicates that annual GDP growth is the only macroeconomic variable exerting a substantial effect on the stayers' probability: as GDP increases, so does the proportion of stayers. Because stayers are the most desirable borrowers, the proposed model should be useful to institutional lenders.

Hidden mover-stayer model for disease progression accounting for misclassified and partially observed diagnostic tests: Application to the natural history of human papillomavirus and cervical precancer.

Hidden Markov models (HMMs) have been proposed to model the natural history of diseases while accounting for misclassification in state identification. We introduce a discrete time HMM for human papillomavirus (HPV) and cervical precancer/cancer where the hidden and observed state spaces are defined by all possible combinations of HPV, cytology, and colposcopy results. Because the population of women undergoing cervical cancer screening is heterogeneous with respect to sexual behavior, and therefore risk of HPV acquisition and subsequent precancers, we use a mover-stayer mixture model that assumes a proportion of the population will stay in the healthy state and are not subject to disease progression. As each state is a combination of three distinct tests that characterize the cervix, partially observed data arise when at least one but not every test is observed. The standard forward-backward algorithm, used for evaluating the E-step within the E-M algorithm for maximum-likelihood estimation of HMMs, cannot incorporate time points with partially observed data. We propose a new forward-backward algorithm that considers all possible fully observed states that could have occurred across a participant's follow-up visits. We apply our method to data from a large management trial for women with low-grade cervical abnormalities. Our simulation study found that our method has relatively little bias and out preforms simpler methods that resulted in larger bias.

Vertex Exchange Method for non-parametric estimation of mixing distributions in logistic mixed models

The conventional normality assumption for the random effects distribution in logistic mixed models can be too restrictive in some applications. In our data example of a longitudinal study modelling employment participation of Australian women, the random effects exhibit non-normality due to a potential mover–stayer scenario. In such a scenario, the women observed to remain in the same initial response state over the study period may consist of two subgroups: latent stayers—those with extremely small probability of transitioning response states—and latent movers, those with a probability of transitioning response states. The similarities between estimating the random effects using non-parametric approaches and mover–stayer models have previously been highlighted. We explore non-parametric approaches to model univariate and bivariate random effects in a potential mover–stayer scenario. As there are limited approaches available to fit the non-parametric maximum likelihood estimate for bivariate random effects in logistic mixed models, we implement the Vertex Exchange Method (VEM) to estimate the random effects in logistic mixed models. The approximation of the non-parametric maximum likelihood estimate derived by the VEM algorithm induces more flexibility of the random effects, identifying regions corresponding to potential latent stayers in the non-employment category in our data example.

Credit Risk Migration and Economic Cycles

The misestimation of rating transition probabilities may lead banks to lend money incoherently with borrowers’ default trajectory, causing both a deterioration in asset quality and higher system distress. Applying a Mover-Stayer model to determine the migration risk of small and medium enterprises, we find that banks are over-estimating their credit risk resulting in excessive regulatory capital. This has important macroeconomic implications due to the fact that holding a large capital buffer is costly for banks and this in turn influences their ability to lend in the wider economy. This conclusion is particularly true during economic downturns with the consequence of exacerbating the cyclicality in risk capital that therefore acts to aggravate economic conditions further. We also explain part of the misevaluation of borrowers and the actual relevant weight of non-performing loans within banking portfolios: some of the prudential requirements, at least as regards EMS credit portfolios, cannot be considered effective as envisaged by the regulators who developed the “new” regulation in response to the most recent crisis. The Mover-Stayers approach helps to reduce calculation inaccuracy when analyzing the historical movements of borrowers’ ratings and consequently, improves the efficacy of the resource allocation process and banking industry stability.

Mover‐stayer model with covariate effects on stayer's probability and mover's transitions

AbstractA discrete time Markov chain assumes that the population is homogeneous, each individual in the population evolves according to the same transition matrix. In contrast, a discrete mover‐stayer (MS) model postulates a simple form of population heterogeneity; in each initial state, there is a proportion of individuals who never leave this state (stayers) and the complementary proportion of individuals who evolve according to a Markov chain (movers). The MS model was extended by specifying the stayer's probability to be a logistic function of an individual's covariates but leaving the same transition matrix for all movers. We further extend the MS model by allowing each mover to have her/his covariates dependent transition matrix. The model for a mover's transition matrix is related to the extant Markov chains mixture model with mixing on the speed of movement of Markov chains. The proposed model is estimated using the expectation‐maximization algorithm and illustrated with a large data set on car loans and the simulation.

Schools can improve motivational quality: Profile transitions across early foreign language learning experiences

Elementary school is as much about developing attitudes as competence. With this fact in mind, the Japanese national government established a plan to enhance elementary school students’ motivation for learning English. The success of this program has, however, not been empirically tested. This study aimed to assess the longitudinal, discrete development of Japanese elementary school students’ motivation for learning English as a foreign language. A cohort of 513 Japanese elementary students participated in the study across 2 years of school. Students responded to surveys regarding the quality of their motivation at three time points, and their engagement at two time points. Latent profile analysis followed by latent profile transition analysis was used to assess the sample for latent subgroups. With subgroups established at three time points, a Mover–Stayer model was tested to estimate the movement of students among the subgroups across three time points and 2 years of elementary school education. Three theoretically consistent latent subgroups were observed at each of the time points. Based on theory and past empirical research, the subgroups (presented from least to most adaptive) were labeled: Poor Quality, High Quantity, and Good Quality. Across the three measurements, an overall shift of students to higher quantity and quality motivational subgroups was observed. This study provides evidence that the low-stakes, high-interest approach currently undertaken may have the desired effect of improving students’ motivation to learn across 2 years of schooling. Implications for both practice and national policy are discussed.

Estimating Default Risk of Bank Loans in Zimbabwe Using the Mover-Stayer Model

This paper estimates default probabilities of bank loans through the use of a mover stayer model, using the data of Zimbabwe. Management of credit risk is an element of financial engineering, which provides safeguard against institutions? financial failure. The study aimed at estimating default probabilities of bank loans through the use of a mover stayer model. In-order to achieve this, the study compared the predictive power of duration method and cohort method in forecasting default risk of bank loans, tested for presence of time homogeneity and determined the model with an upper hand between the Mover stayer model and the Markov Chain Model in gauging default risk. It was concluded that the cohort approach has an upper hand than the duration approach and that there was time inhomogeneity. There was also significant evidence that the mover-stayer model is a superior and effective way of estimating the risk of default. The effectiveness was shown through the process of back testing. The forecasted results for 2014 were in line with the actual 2014 default results hence the model called the Mover Stayer effectively and competently predicted the risk of default of bank advances and loans.

Conditional Joint Probability Distributions of First Exit Times to Overlapping Absorbing Sets of the Mixture of Markov Jump Processes

New results on conditional joint probability distributions of first exit times are presented for a continuous-time stochastic process defined as the mixture of Markov jump processes moving at different speeds on the same finite state space, while the mixture occurs at a random time. Such mixture was first proposed by Frydman \cite{Frydman2005} and Frydman and Schuermann \cite{Frydman2008} as a generalization of the mover-stayer model of Blumen et at. \cite{Blumen}, and was recently extended by Surya \cite{Surya2018}, in which explicit distributional identities of the process are given, in particular in the presence of an absorbing state. We revisit \cite{Surya2018} for a finite mixture with overlapping absorbing sets. The contribution of this paper is two fold. First, we generalize distributional properties of the mixture discussed in \cite{Frydman2008} and \cite{Surya2018}. Secondly, we give distributional identities of the first exit times explicitly in terms of intensity matrices of the underlying Markov processes and the Bayesian updates of switching probability and of the probability distribution of states, despite the fact that the mixture itself is non-Markov. They form non-stationary functions of time and have the ability to capture heterogeneity and path dependence when conditioning on the available information (either full or partial) of the process. In particular, initial profile of the distributions forms of a generalized mixture of multivariate phase-type distributions of Assaf et al. \cite{Assaf1984}. When the underlying processes move at the same speed, in which case the mixture becomes a simple Markov process, these features are removed, and the initial distributions reduce to \cite{Assaf1984}. Some explicit and numerical examples are discussed to illustrate the main results.

Supporting interest in a study domain: A longitudinal test of the interplay between interest, utility-value, and competence beliefs

The current study used a longitudinal design to model initial interest and utility-value as antecedents of developing interest and course proficiency. Using measures from four time points across one academic year and competency assessed at the beginning of the previous year, we examined direct and mediated contributions of utility-value, self-efficacy, and self-concept for the development of domain interest. Japanese tertiary students (n = 614; Female = 129) undertaking a compulsory year-long study of English as a foreign language participated. Students reported motivation (interest, utility-value and competence beliefs of self-efficacy and self-concept) for studying English as a foreign language. In addition, the design allowed detection of reciprocal effects: the forward effect of interest on competence beliefs and in turn the forward effects of competence beliefs on interest. Initial domain interest indicated direct and/or mediated effects for all constructs, while self-efficacy indicated a reciprocal relationship with domain interest. Profile analyses (LPA) identified 3 motivation profiles that were stable across two semesters. Testing a mover-stayer model (LPTA) indicated some movement between the low and medium intensity profiles of motivation.

Does France have a fuel poverty trap?

In this article, we focus on fuel poverty dynamics by answering two questions: Does France have a fuel poverty trap and what are the determinants of staying in or moving out of fuel poverty? First, we define three states into which individuals may be placed, which are as follows: the non-fuel-poverty state, the fuel poverty state and the severe fuel poverty state. Second, we use a mover-stayer model that divides the population into the following two types of individuals: those who remain in the same state during the observation period (the stayers) and those who move across states (the movers). This model applies to longitudinal data from mainland France showing that fuel poverty is not an absorbing state. Indeed, a majority of the fuel-poor and the severely fuel-poor move to another, better state. Therefore, we can argue that France has no fuel poverty trap. Using two econometric models (logit and multinomial logit), we identify the stability and mobility determinants in different states. As expected, there is a relationship between income and the likelihood of an individual remaining in a particular state. Furthermore, poor housing implies a greater likelihood of stability in fuel poverty or severe fuel poverty. Another result is that deterioration in fuel poverty status seems to stem more from difficult financial situations than from bad dwelling conditions.

Estimation and status prediction in a discrete mover‐stayer model with covariate effects on stayer's probability

A discrete‐time mover‐stayer (MS) model is an extension of a discrete‐time Markov chain, which assumes a simple form of population heterogeneity. The individuals in the population are either stayers, who never leave their initial states or movers who move according to a Markov chain. We, in turn, propose an extension of the MS model by specifying the stayer's probability as a logistic function of an individual's covariates. Such extension has been recently discussed for a continuous time MS but has not been considered before for a discrete time one. This extension allows for an in‐sample classification of subjects who never left their initial states into stayers or movers. The parameters of an extended MS model are estimated using the expectation‐maximization algorithm. A novel bootstrap procedure is proposed for out of sample validation of the in‐sample classification. The bootstrap procedure is also applied to validate the in‐sample classification with respect to a more general dichotomy than the MS one. The developed methods are illustrated with the data set on installment loans. But they can be applied more broadly in credit risk area, where prediction of creditworthiness of a loan borrower or lessee is of major interest.

Analysis of panel data under hidden mover-stayer models.

Analysis of panel data is often challenged by the presence of heterogeneity and state misclassification. In this paper, we propose a hidden mover-stayer model to facilitate heterogeneity for a population that consists of two subpopulations each of movers or of stayers and to simultaneously account for state misclassification. We develop an inference procedure based on the expectation-maximization algorithm by treating the mover-stayer indicator and underlying true states as latent variables. We evaluate the performance of the proposed method and investigate the impact of ignoring misclassification through simulation studies. The proposed method is applied to analyze the data arising from the Waterloo Smoking Prevention Project. Copyright © 2017 John Wiley & Sons, Ltd.

Movers and Stayers in The Farming Sector: Accounting for Unobserved Heterogeneity in Structural Change

SummaryThe paper investigates whether accounting for unobserved heterogeneity in farms' size transition processes improves the representation of structural change in agriculture. Considering a mixture of two types of farm, the mover–stayer model is applied for the first time in an agricultural economics context. The maximum likelihood method and the expectation–maximization algorithm are used to estimate the model's parameters. An empirical application to a panel of French farms from 2000 to 2013 shows that the mover–stayer model outperforms the homogeneous Markov chain model in recovering the transition process and predicting the future distribution of farm sizes.

Revealing transition patterns between mono- and multimodal travel patterns over time: A mover-stayer model

Recent empirical evidence suggests that travellers are becoming increasingly multimodal. Coinciding with this trend, a growing interest can be observed in the transport literature to study the concept of multimodality. Most studies, in this regard, have focused on assessing the determinants of multimodal travel behaviour. While it is interesting to know which factors, at a certain moment in time, affect the membership of mono/multimodal travel patterns, one general omission in the current literature relates to the questions how and why travellers switch between the mono/multimodal travel patterns over time. This study aims to fill this knowledge gap. To this end, a mixture latent Markov model is specified and estimated using data from the German mobility panel. Our mixture latent Markov models consist of latent travel patterns as well as latent mobility styles. To acquire insights on changes in travel behaviour various model specifications are tested. The travel data is best explained by a model consisting of five latent travel patterns and three mobility styles. The five travel patterns are can be conceived as (1) strict car users, (2) public transport and occasional car users, (3) car passengers, (4) car and bicycle users and (5) bicycle and occasional public transport users, and the three underlying mobility styles are identified as (1) habitual travellers, who stay in their respective pattern for three consecutive years, (2) car (in)dependent choice travellers, who switch within car and non-car patterns, and (3) car users with an alternative mode preference, who switch between car and noncar patterns. Overall, it is concluded that mixture latent Markov models are effective to reveal (heterogeneity in) transition patterns.

The effect of lifelong learning on men’s wages

This paper develops a model of earnings and applies this to an examination of the effect of lifelong learning on men’s wages. Using data from the British Household Panel Survey, a variant of the mover–stayer model is developed in which hourly wages are either taken from a stationary distribution (movers) or closely related to the hourly wage one year earlier (stayers). Mover–stayer status is not observed, and we therefore model wages using an endogenous switching regression, estimated by maximum likelihood. Methodologically, the results support the mover–stayer characterisation since the restrictions required for the simpler specifications popular in the literature are rejected. Substantively, simulation of the estimated model shows some statistically significant effects from acquiring qualifications of a higher level than those previously held, but not from acquiring qualifications of the same level.

Credit Risk Measurement Based on the Markov Chain

Credit migration matrices are often used in many credit risk and pricing application, and typically assumed to be generated by a simple Markov process. This paper is going to analyze the basic elements of credit risk research, and Maximum Likelihood estimation will be adopted to estimate the Mover-Stayer model’s parameters in this paper. Furthermore, the recursive method will be used to compute the Maximum Likelihood estimator, and the numerical results can illustrate the strength of the Mover-Stayer model on credit risk analysis. We also use the hypotheses to prove that the Markov chain suit for the data against the hypotheses that the Mover-Stayer model more suitable for the data. Finally, we will make some comparisons according to the output of the program, and obtain some conclusions. The Mover-Stayer Model is more suitable against according the numbered result.