Limited Dependent Variable Models Research Articles

Bayesian Estimation of Fixed Effects Models with Large Datasets*

AbstractIn hierarchical prior longitudinal models, random effects are estimated by the Gibbs sampler. We show that fixed effects can be handled by a similar Gibbs sampler under a diffuse prior on the unobserved heterogeneity. The dummy variable approach for fixed effects is computationally intensive and has the out‐of‐memory risk, while the Gibbs sampler can reproduce the dummy variable estimator without creating dummy variables, and therefore avoids the memory burden. Compared to alternating projections and other classical approaches, our method simplifies both inference and estimation of the limited dependent variable models with fixed effects. The proposed method is applied to a real‐world mortgage dataset for classification with three‐way fixed effects on banks, regions, and loan purposes.

Protocol for a longitudinal study examining the trajectory of COVID-19, post-COVID, multidimensional disadvantage and health-related quality of life in India: the IndiQol Project

IntroductionThe COVID-19 pandemic has raised concerns about the persistence of symptoms after infection, commonly referred to as ‘post-COVID’ or ‘long-COVID’. While countries in high-resource countries have highlighted the increased risk...

Mapping functions for the PHQ-9 and GAD-7 to generate EQ-5D-3L for economic evaluation.

Generic preferenced-based measures, such as EQ-5D-3L, that are used to estimate quality adjusted life years (QALYs) for economic evaluation are not always available in clinical trials. Predicting EQ-5D-3L values from the commonly used Patient Health Questionnaire 9 (PHQ-9) and Generalised Anxiety Disorder-7 (GAD-7) would allow estimation of QALYs from such trials. The aim was to provide mapping functions to estimate EQ-5D-3L from PHQ-9 and GAD-7 to facilitate economic evaluation. Data was drawn from four trials of patients with symptoms of depression testing collaborative care or computerised cognitive behavioural therapy. Patients completed PHQ-9, GAD-7, and EQ-5D-3L at different timepoints. Mapping was undertaken using adjusted limited dependent variable mixture models (ALDVMM), ordinary least squares (OLS), and Tobit models based on PHQ-9, GAD-7 scores or questions, and age to predict EQ-5D-3L utilities. Models were selected based on mean error (ME), mean absolute error (MAE), root mean squared error (RMSE), model goodness of fit, and visual inspection of the predictions. There were 5583 and 3942 observations for EQ-5D-3L combined with PHQ-9 and GAD-7 respectively. ALDVMM models had low ME ( ≤|0.0018|) and MAE ranging from 0.189 to 0.192, while RMSE was from 0.251 to 0.254 and had better predictions than OLS and Tobit models. ALDVMM models with four components based on PHQ-9 and GAD-7 scores are recommended for estimating EQ-5D-3L utilities. Recommended mapping functions provide users with an approach to estimate EQ-5D-3L utilities for economic evaluation using PHQ-9, GAD-7, or both scores where they have been used together.

Ethnolinguistic diversity, quality of local public institutions, and firm-level innovation

Institutional quality is crucial for innovation and economic growth. In this article, we exploit historical linguistic differences across Slovenian municipalities between the Italian, German, and Slovenian-speaking population prior to World War 1, as a plausible exogenous source of variation in firm-level innovation to estimate the effect of institutional quality on innovation. Employing a set of limited dependent variable and instrumental variable models, we show that greater historical exposure to multilingualism is associated with markedly better quality of government and provision of public goods, more impartial local government administration, and lower prevalence of corruption, which in turn predicts systematically more vibrant economic activity, greater economic complexity, and higher rates of firm-level innovation at the local level. The estimated effects are robust to a variety of specification checks and do not appear to be sensitive to the choice of ethnic and linguistic diversity measures.

Catalogues of EQ-5D-3L Health-Related Quality of Life Scores for 199 Chronic Conditions and Health Risks for Use in the UK and the USA.

Health-related quality of life (HRQoL) measures are essential in economic evaluation, but sometimes primary sources are unavailable, and information from secondary sources is required. Existing HRQoL UK/US catalogues are based on earlier diagnosis classification systems, amongst other issues. A recently published Danish catalogue merged EQ-5D-3L data from national health surveys with national registers containing patient information on ICD-10 diagnoses, healthcare activities and socio-demographics. To provide (1) UK/US EQ-5D-3L-based HRQoL utility population catalogues for 199 chronic conditions on the basis of ICD-10 codes and health risks and (2) regression models controlling for age, sex, comorbidities and health risks to enable predictions in other populations. UK and US EQ-5D-3L value sets were applied to the EQ-5D-3L responses of the Danish dataset and modelled using adjusted limited dependent variable mixture models (ALDVMMs). Unadjusted mean utilities, percentiles and adjusted disutilities based on two ALDVMMs with different control variables were provided for both countries. Diseases from groups M, G, and F consistently had the smallest utilities and the largest negative disutilities: fibromyalgia (M797), sclerosis (G35), rheumatism (M790), dorsalgia (M54), cerebral palsy (G80-G83), post-traumatic stress disorder (F431), dementia (F00-2), and depression (F32, etc.). Risk factors, including stress, loneliness, and BMI30+, were also associated with lower HRQoL. This study provides comprehensive catalogues of UK/US EQ-5D-3L HRQoL utilities. Results are relevant in cost-effectiveness analysis, for NICE submissions, and for comparing and identifying facets of disease burden.

Enabling QALY estimation in mental health trials and care settings: mapping from the PHQ-9 and GAD-7 to the ReQoL-UI or EQ-5D-5L using mixture models

PurposePatient-reported outcome measures (PROMs) are commonly collected in trials and some care settings, but preference-based PROMs required for economic evaluation are often missing. For these situations, mapping models are needed to predict preference-based (aka utility) scores. Our objective is to develop a series of mapping models to predict preference-based scores from two mental health PROMs: Patient Health Questionnaire-9 (PHQ-9; depression) and Generalised Anxiety Questionnaire-7 (GAD-7; anxiety). We focus on preference-based scores for the more physical-health-focussed EQ-5D (five-level England and US value set, and three-level UK cross-walk) and more mental-health-focussed Recovering Quality-of-Life Utility Index (ReQoL-UI).MethodsWe used trial data from the Improving Access to Psychological Therapies (IAPT) mental health services (now called NHS Talking Therapies), England, with a focus on people with depression and/or anxiety caseness. We estimated adjusted limited dependent variable or beta mixture models (ALDVMMs or Betamix, respectively) using GAD-7, PHQ-9, age, and sex as covariates. We followed ISPOR mapping guidance, including assessing model fit using statistical and graphical techniques.ResultsOver six data collection time-points between baseline and 12-months, 1340 observed values (N ≤ 353) were available for analysis. The best fitting ALDVMMs had 4-components with covariates of PHQ-9, GAD-7, sex, and age; age was not a probability variable for the final ReQoL-UI mapping model. Betamix had practical benefits over ALDVMMs only when mapping to the US value set.ConclusionOur mapping functions can predict EQ-5D-5L or ReQoL-UI related utility scores for QALY estimation as a function of variables routinely collected within mental health services or trials, such as the PHQ-9 and/or GAD-7.

Local Governments’ Adoption of Innovative Infrastructure Finance Tool: Evidence From Pennsylvania Municipalities

State Infrastructure Banks (SIBs) are established to provide low-interest loans and credit enhancements to assist local governments in financing transportation projects. SIB loans, one of their core products, are low-cost and low-risk when compared to traditional capital finance tools. However, SIB loans are still rarely used by local communities. This study investigates the determinants of local government adoption of SIB loans among Pennsylvania municipalities from 2008 to 2015. Using limited dependent variable models, we discover that infrastructure demands, prior experiences, and neighboring adoptions are all positively associated with municipalities’ likelihood of applying for SIB loans as well as the intensity of loan usage, whereas fund balance reduces the probability of applying for SIB loans. We also find that as fund balance increases, the positive impact of infrastructure demands diminishes.

Catalog of EQ-5D-3L Health-Related Quality-of-Life Scores for 199 Chronic Conditions and Health Risks in Denmark.

A Danish national representative catalog of health-related quality-of-life scores for 199 chronic conditions is presented, which provides population estimates for chronic conditions subgroups that can be used for health economic evaluation.Two separate regression models of EQ-5D-3L utility scores with different sets of control variables are estimated to allow researchers to adjust for differences in the composition of the subgroups and provide a tool that can be used in other settings.Results indicate that health-related quality of life varies across disease groups but is lowest for renal disease, mental and behavioral disorders, benign neoplasms and diseases of the blood, digestive systems, and nervous systems.Health risks and lifestyle factors such as perceived stress, loneliness, and a large body mass index are highly correlated with health-related quality of life, and, in many cases, the correlation is higher than with individual diseases.

Modeling Participation and Consumption in the Greek Interurban Public Transportation Market

This article investigates the Greek household travel demand for domestic interurban public transportation using cross-sectional micro-data from a countrywide Household Budget Survey. A number of limited dependent variable models, including the Heckit, Two-Part, and Double-Hurdle models, are implemented to jointly estimate the probability of selecting a specific mode and the amount of using it. The results provide useful insight into the existence of feedback relationships between the decision-making mechanisms of mode selection and amount of usage, and they demonstrate the predominant effect of income on the demand for coaches, railways, airplanes, and coast-wise sea ferries.

Developing decision support tools incorporating personalised predictions of likely visual benefit versus harm for cataract surgery: research programme

Developing decision support tools incorporating personalised predictions of likely visual benefit versus harm for cataract surgery: research programme

Mapping the Oxford Shoulder Score onto the EQ-5D utility index

PurposeIn order to enable cost-utility analysis of shoulder pain conditions and treatments, this study aimed to develop and evaluate mapping algorithms to estimate the EQ-5D health index from the Oxford Shoulder Score (OSS) when health outcomes are only assessed with the OSS.Methods5437 paired OSS and EQ-5D questionnaire responses from four national multicentre randomised controlled trials investigating different shoulder pathologies and treatments were split into training and testing samples. Separate EQ-5D-3L and EQ-5D-5L analyses were undertaken. Transfer to utility (TTU) regression (univariate linear, polynomial, spline, multivariable linear, two-part logistic-linear, tobit and adjusted limited dependent variable mixture models) and response mapping (ordered logistic regression and seemingly unrelated regression (SUR)) models were developed on the training sample. These were internally validated, and their performance evaluated on the testing sample. Model performance was evaluated over 100-fold repeated training–testing sample splits.ResultsFor the EQ-5D-3L analysis, the multivariable linear and splines models had the lowest mean square error (MSE) of 0.0415. The SUR model had the lowest mean absolute error (MAE) of 0.136. Model performance was greatest in the mid-range and best health states, and lowest in poor health states.For the EQ-5D-5L analyses, the multivariable linear and splines models had the lowest MSE (0.0241–0.0278) while the SUR models had the lowest MAE (0.105–0.113).ConclusionThe developed models now allow accurate estimation of the EQ-5D health index when only the OSS responses are available as a measure of patient-reported health outcome.

Generating EQ-5D-5L health utility scores from BASDAI and BASFI: a mapping study in patients with axial spondyloarthritis using longitudinal UK registry data

BackgroundPreference-based health-state utility values (HSUVs), such as the EuroQol five-dimensional questionnaire (EQ-5D-5L), are needed to calculate quality-adjusted life-years (QALYs) for cost-effectiveness analyses. However, these are rarely used in clinical trials of interventions in axial spondyloarthritis (axSpA). In these cases, mapping can be used to predict HSUVs.ObjectiveTo develop mapping algorithms to estimate EQ-5D-5L HSUVs from the Bath Ankylosing Disease Activity Index (BASDAI) and the Bath Ankylosing Spondylitis Functional Index (BASFI).MethodsData from the British Society for Rheumatology Biologics Register in Ankylosing Spondylitis (BSRBR-AS) provided 5122 observations with complete BASDAI, BASFI, and EQ-5D-5L responses covering the full range of disease severity. We compared direct mapping using adjusted limited dependent variable mixture models (ALDVMMs) and optional inclusion of the gap between full health and the next feasible value with indirect response mapping using ordered probit (OPROBIT) and generalised ordered probit (GOPROBIT) models. Explanatory variables included BASDAI, BASFI, and age. Metrics to assess model goodness-of-fit and performance/accuracy included Akaike and Bayesian information criteria (AIC/BIC), mean absolute error (MAE) and root mean square error (RMSE), plotting predictive vs. observed estimates across the range of BASDAI/BASFI and comparing simulated data with the original data set for the preferred/best model.ResultsOverall, the ALDVMM models that did not formally include the gap between full health and the next feasible value outperformed those that did. The four-component mixture models (with squared terms included) performed better than the three-component models. Response mapping using GOPROBIT (no squared terms included) or OPROBIT (with squared terms included) offered the next best performing models after the three-component ALDVMM (with squared terms). Simulated data of the preferred model (ALDVMM with four-components) did not significantly underestimate uncertainty across most of the range of EQ-5D-5L values, however the proportion of data at full health was underrepresented, likely due in part to model fitting on a small number of observations at this point in the actual data (4%).ConclusionsThe mapping algorithms developed in this study enabled the generation of EQ-5D-5L utilities from BASDAI/BASFI. The indirect mapping equations reported for the EQ-5D-5L facilitate the calculation of the EQ-5D-5L utility scores using other UK and country-specific value sets.

Self-Employment, Gender and Cultural Traits

Though the gap between female and male entrepreneurship has been narrowing globally, it is still evident with female rates lagging behind those of males. While existing literature has identified several obstacles to female entrepreneurship, the role of cultural traits has not yet been adequately explored. More importantly, lacking from the literature is a close investigation of female entrepreneurial choices using individual level data across countries. Employing World Values Survey data, an extensive longitudinal panel study of countries over time with over 300,000 individual level observations, we look at how cultural indicators impact female entrepreneurship. Using probit limited dependent variable models, we analyze specifically how cultural indicators impact female entrepreneurship, using measures of independence, obedience, and control over one's own life as our cultural indicators. In our analysis, we control for age, marital status, social class, town size, and level of education, as these factors have an effect on the decision to be self-employed. We also conducted robustness analysis using alternate cultural indicator variables to look for any change when compared to our benchmark findings. Our findings show that being a female lowers the probability of being self-employed. This supports the existing literature that shows a gap, albeit narrowing, between male and female entrepreneurship. Our main set of results also show that the cultural traits of independence and sense of control over one's life both help alleviate the negative impact of gender (being a female) on entrepreneurial choices. As a society, valuing obedience has the opposite impact – it magnifies the negative effect of being female on the probability of being self-employed. These findings were shown to be robust when we incorporated alternate cultural indicator variables. Our findings suggest that consideration should be given to cultural traits in the context of development outcomes. Because cultural traits can be difficult to change, our results suggest that as policy makers implement interventions to promote self-employment among females, they should be aware of the relevant cultural factors of the area and how these interact with female entrepreneurship. Policy can then be tailored to the cultural environment to maximize the intended effect on female entrepreneurship rates.

Examining the Effect of Short-Term Affect on Farmers’ Risk and Time Preferences in Financial Decision-Making

Farmers regularly make intertemporal decisions under risk or uncertainty. To improve how farmers behave when faced with decisions that have financial consequences, there is a need for a deeper understanding of farmers’ risk and time preferences. While the relationship between individual components of affect and risk preferences is well documented, the same cannot be said for holistic measures of affect on one hand, and for affect and time preferences on the other hand. The data analysed in this paper is the 2014–2015 Indonesian Family Life Survey Wave 5. The survey included experimental measures designed to elicit both risk and time preferences from the same subjects. We analysed the data using limited dependent variable regression models. Our findings strengthen what is known about the affect infusion model. With increased pleasant affect, farmers’ willingness to take risks increases significantly. The results also suggest that pleasant affect is associated with increased odds that farmers will choose future rewards in the long horizon but had no statistically significant effect on the short horizon. The practical implications are that an experience of pleasant affect before decision-making may cause the decision-maker (DM) to perceive a prospect as having high benefits and low risks. Pleasant affect may also induce lower sensitivity towards losses and play the role of a buffer which reduces the immediate negative impact of information that otherwise would prevent the DM from focusing on the long-term. JEL Classifications: C93, D81, D91

Mapping of the acromegaly quality of life questionnaire to ED-5D-5L index score among patients with acromegaly.

This study aimed to develop a mapping function that links the acromegaly quality of life (AcroQoL) questionnaire to EQ-5D-5L to obtain a preference-based utility value to inform economic evaluation. A nationwide cross-sectional questionnaire survey among patients with acromegaly was conducted online in China during 17 December 2019 to 6 January 2020. The study sample was randomly divided into a training set and a validation set. Ordinary least squares (OLS), Tobit, beta-based mixture, and adjusted limited dependent variable mixture models were tested for development of the function in the training set. Total and subscale scores and individual items of AcroQoL were included as predictors in the models along with their squared terms and demographic and clinical characteristics, and selected by backward stepwise selection. The root mean square error, mean absolute error, Akaike's information criterion, Bayesian information criterion and adjusted R-square were used to assess goodness of fit and predictive ability of the models. There were 424 adult patients with acromegaly eligible for this analysis. Average EQ-5D-5L index score and AcroQoL score for them was 0.82 (SD = 0.15) and 44.3 (SD = 22.9), respectively. A total of 60 candidate models were tested. Considering model simplicity and predictive ability in both training and validation set, the best model was the OLS model using scores of physical dimension and its square term as predictors. A validated mapping function was developed in this study for estimating EQ-5D scores using AcroQoL outcomes. Its external validity can be further tested in other population with Acromegaly.

How does cleaner energy transition influence standard of living and natural resources conservation? A study of households’ perceptions in rural Odisha, India

While importance of cleaner cooking fuels for improving quality of life and facilitating social inclusion and ecological sustainability is well-recognized, success of the initiative depends on beneficiaries’ perceptions about the potential benefits. Here, we examine how the beneficiaries perceive about the benefits of the Pradhan Mantri Ujjwala Yojana (PMUY), an initiative of the Government of India, which aims at providing subsidised connections of liquefied petroleum gas (LPG) to the poor households of the country. Perceptions are examined in respect of changes in standard of living and natural resource conservation. Based on primary data and information collected from five villages of the Puri district of Odisha, it is found that beneficiaries perceive only marginal or no change in standard of living after LPG connection in India. Further, the estimated limited dependent variable models show that such perceptions depend on household heads’ education, subsidy on LPG and changes in firewood use. However, occupation or household income does not have any significant impact on perceptions. Efforts should, therefore, be made towards raising awareness of beneficiaries, making LPG cheaper and restricting firewood use for changing households’ perceptions about the benefits of LPG toward greater success of the PMUY.

Consumer Preferences for Electric Vehicle Charging Services: Evidence from NIO’s ‘Worry Free Plan’

Range anxiety restrains the widespread adoption of plug-in electric vehicles. This paper utilises novel survey data on NIO ES8 owners in order to investigate whether preferences for innovative electric vehicle charging services (EVCS) are augmented by range anxiety. Our limited dependent variable models draw upon NIO ES8 owners’ revealed and stated preferences for the Worry Free Plan. Objective measures of range are found to feed into consumers’ stated preferences, whilst the owners’ subjective concerns appear to statistically dominate the consumers’ revealed preferences for this service. A suite of specification checks supports the view that EVCS primarily overcomes the psychological foundations of range anxiety, elucidating insights for the development of innovative and sustainable service-based business models and policy design.

Mapping to Quality of Life and Capability Measures in Cataract Surgery Patients: From Cat-PROM5 to EQ-5D-3L, EQ-5D-5L, and ICECAP-O Using Mixture Modelling.

Objectives. Cataract is a prevalent and potentially blinding eye condition. Cataract surgery, the only proven treatment for this condition, is a very frequently undertaken procedure. The objective of this analysis was to develop a mapping algorithm that could be used to predict quality of life and capability scores from the Cat-PROM5, a newly developed, validated patient-reported outcome measure for patients undergoing cataract surgery. Methods. We estimated linear models and adjusted limited dependent variable mixture models. Data were taken from the Predict-CAT cohort of up to 1181 patients undergoing cataract surgery at two sites in England. The Cat-PROM5 was mapped to two quality of life measures (EQ-5D-3L and EQ-5D-5L) and one capability measure (ICECAP-O). All patients reported ICECAP-O and one or other of the EQ-5D measures both before and after cataract surgery. Model performance was assessed using likelihood statistics, graphical inspections of model fit, and error measurements. Results. Adjusted limited dependent variable mixture models dominated linear models on all performance criteria. Mixture models offered very good fit. Three component models that allowed component membership to be a function of covariates (age, sex, and diabetic status depending on specification and outcome measure) and which conditioned on covariates offered the best performance in almost all cases. An exception was the EQ-5D-5L post-surgery for which a two-component model was selected. Conclusions. Mapping from Cat-PROM5 to quality of life and capability measures using adjusted limited dependent variable mixture models is feasible, and the estimates can be used to support cost-effectiveness analysis in relation to cataract care. Mixture models performed strongly for both quality of life outcomes and capability outcomes.

Determinants of adoption of cleaner cooking energy: Experience of the Pradhan Mantri Ujjwala Yojana in rural Odisha, India

Since its inception, the Pradhan Mantri Ujjwala Yojana (PMUY) of the Government of India has provided subsidized liquefied petroleum gas (LPG) connections to many poor households for enhancing use of LPG as a cooking fuel. However, along with such large LPG connections, it is also necessary to understand how the beneficiaries have adopted the same. This paper examines beneficiary households’ response to the PMUY in respect of actual use of LPG and identifies the underlying factors in rural areas of the Indian state of Odisha. Using descriptive statistics and estimating limited dependent variable models the paper finds significant positive impact of household heads’ education and amount of subsidy on actual use of LPG, whereas general category households have lower adoption of the same. Further, greater availability of kerosene also limits adoption of LPG. Importantly, household income does not influence adoption of this cleaner fuel. The findings of the paper, therefore, have significant implications for fine tuning of policies and institutions towards cleaner energy transition in rural India, particularly in respect of enhancing relative price and awareness about benefits of LPG and its delivery mechanisms.

Innovation in firms, resilience and the economic downturn: Insights from CIS data in Portugal

AbstractThere is an interest in understanding the effect of economic crises such as the one that hit the financial markets in the late 2000s, on the innovation performance of countries and regions. This paper introduces the concept of “resilience of innovation” to illustrate how the economic slowdown affects firms' behaviour in terms of their ability to maintain and develop innovative activities and deploy product and process innovation. Using Portugal as a case study—an EU member‐state that was heavily affected by the economic downturn—this paper explores the data collected from four waves of the Community Innovation Survey from 2006 to 2012. It presents two‐stage limited dependent variable models to understand the changing impacts of structural factors, innovative activities and strategies in terms of exploration and exploitation of knowledge on the development of product and process innovation. We find knowledge exploration to be particularly important for product innovation, while exploitation is a strong determinant for process innovation. Size, market knowledge sources and public funding for innovation are positively associated with both types of innovation in the peak of the crisis. This reiterates the importance of innovation support efforts to mitigate the effects of economic shocks and boost recovery.