Full Information Maximum Likelihood Approach Research Articles

Comparisons of statistical methods for handling attrition in a follow-up visit with complex survey sampling.

Design-based analysis, which accounts for the design features of the study, is commonly used to conduct data analysis in studies with complex survey sampling, such as the Hispanic Community Health Study/Study of Latinos (HCHS/SOL). In this type of longitudinal study, attrition has often been a problem. Although there have been various statistical approaches proposed to handle attrition, such as inverse probability weighting (IPW), non-response cell weighting (NRCW), multiple imputation (MI), and full information maximum likelihood (FIML) approach, there has not been a systematic assessment of these methods to compare their performance in design-based analyses. In this article, we perform extensive simulation studies and compare the performance of different missing data methods in linear and generalized linear population models, and under different missing data mechanism. We find that the design-based analysis is able to produce valid estimation and statistical inference when the missing data are handled appropriately using IPW, NRCW, MI, or FIML approach under missing-completely-at-random or missing-at-random missing mechanism and when the missingness model is correctly specified or over-specified. We also illustrate the use of these methods using data from HCHS/SOL.

Multilevel modelling approach to analysing life course socioeconomic status and understanding missingness

This paper investigated the extent to which parental socioeconomic status was associated with life course socioeconomic status heterogeneity between adult cohort members of the 1958 National Child Development Study and how this association differed depending on methods used to address longitudinal missing data. We compared three variants of the full information maximum likelihood approach, namely available case, complete case and partially observed case and two methods designed to compensate for missing at random data, namely multilevel multiple imputation and multiple imputation chained equations. Our results highlighted the important contribution of parental socioeconomic status in explaining the divergence in achieved socioeconomic status over the adult life course, how the available case approach increasingly overestimated socioeconomic attainment as age increased and survey sample size decreased and how the complete case approach downwardly biased the effect of parental socioeconomic status on adult socioeconomic status.

Evaluating FIML and multiple imputation in joint ordinal-continuous measurements models with missing data.

Missing data is a common occurrence in confirmatory factor analysis (CFA). Much work had evaluated the performance of different techniques when all observed variables were either continuous or ordinal. However, few have investigated these techniques when observed variables are a mix of continuous and ordinal variables. This study investigated the performance of four approaches to handling missing data in these models: a joint ordinal-continuous full information maximum likelihood (FIML) approach and three multiple imputation approaches (fully conditional specification, fully conditional specification with latent variable formulation, and expectation-maximization with bootstrapping) combined with the weighted least squares with mean and variance adjustment (WLSMV) estimator. In a Monte-Carlo simulation, the FIML approach produced unbiased estimations of factor loadings and standard errors in almost all conditions. Fully conditional specification combined with WLSMV was second best, producing accurate estimates when the sample size was large. However, FIML encountered slight non-convergence issues when certain ordinal categories have extremely low frequencies, which is typical of skewed data. If the sample is large, fully conditional specification combined with weighted least squares is recommended when the FIML approach is not feasible (e.g., non-convergence, impractical computation durations, and variables that predict missingness are not of interest to the analysis).

Does the first job affect current youth working status in Bangladesh?

PurposeThis paper evaluates how the first job when individuals entered the labor market affects the probability of youth being currently employed in formal or informal work in Bangladesh.Design/methodology/approachThe analysis is based on data from the ILO School-to-Work Transition Surveys. The authors use a full-information maximum likelihood approach to estimate a two-equation model, which accounts for selection into the labor market when estimating the impact of entry status on current work outcomes. The main equation outcome follows a multinomial distribution thus avoiding a priori assumptions about the level of individual’s utility associated with each work status.FindingsThe authors find that entering the labor market in a vulnerable employment position (i.e. contributing family work or self-employment) traps into vulnerable employment and prevents the transition to both informal and, especially, formal paid work. This finding holds when accounting for endogeneity of the entry status and it is valid both in the short and in the long run. Young women are less likely to enter the labor market, and once entered they are less likely to access formal paid wok and more likely to being inactive than young men. Low education anticipates the entry in the labor market, but it is detrimental for future employment prospects.Originality/valueThe findings indicate the presence of labor market segmentation between vulnerable and non-vulnerable employment and suggest the endpoint quality of the school-to-work transition is crucial for later employment prospects of Bangladeshi youth.

A control-function approach to correct for endogeneity in discrete choice models estimated on SP-off-RP data and contrasts with an earlier FIML approach by Train & Wilson

It is common practice to build Stated Preference (SP) attributes and alternatives from observed Revealed Preference (RP) choices with a view to increasing realism. While many surveys pivot all alternatives around an observed choice, others use more adaptive approaches in which changes are made depending on what alternative was chosen in the RP setting. For example, in SP-off-RP data, the alternative chosen in the RP setting is worsened in the SP setting and other alternatives are improved to induce a change in behaviour. This facilitates the creation of meaningful trade-offs or tipping points but introduces endogeneity. This source of endogeneity was largely ignored until Train and Wilson (T&W) proposed a full information maximum likelihood (FIML) solution that can be implemented with simulation. In this article, we propose a limited information maximum likelihood (LIML) approach to address the SP-off-RP problem using a method which does not need simulation, can be applied with standard software and uses data that is already available for the stated problem. The proposed method is an application of the control-function (CF) method to correct for endogeneity in discrete choice models, using the RP attributes as instrumental variables. We discuss the theoretical and practical advantages and disadvantages of the CF and T&W methods and illustrate them using Monte Carlo and real data. Results show that, while the T&W method may be more efficient in theory, it may however fail to retrieve consistent estimators when it does not account properly for the data generation process if, e.g., an exogenous source of correlation among the SP choice tasks exists. On the other hand, the CF is more robust, i.e. less sensitive, to the data generation process assumptions, and is considerably easier to apply with standard software and does not require simulation, facilitating its adoption and the more extensive use of SP-off-RP data.

Examining Validity-Related Correlations and Their Differences Under Assumption Violations.

A procedure for evaluation of validity related coefficients and their differences is discussed, which is applicable when one or more frequently used assumptions in empirical educational, behavioral and social research are violated. The method is developed within the framework of the latent variable modeling methodology and accomplishes point and interval estimation of convergent and discriminant correlations as well as differences between them in cases of incomplete data sets with data not missing at random, nonnormality, and clustering effects. The procedure uses the full information maximum likelihood approach to model fitting and parameter estimation, does not assume availability of multiple indicators for underlying latent constructs, includes auxiliary variables, and accounts for within-group correlations on main response variables resulting from nesting effects involving studied respondents. The outlined procedure is illustrated on empirical data from a study using tertiary education entrance examination measures.

Robust Respondents and Lost Limitations: The Implications of Nonrandom Missingness for the Estimation of Health Trajectories.

We offer a strategy for quantifying the impact of mortality and attrition on inferences from later-life health trajectory models. Using latent class growth analysis (LCGA), we identify functional limitation trajectory classes in the Health and Retirement Study. We compare results from complete case and full information maximum likelihood (FIML) analyses, and demonstrate a method for producing upper- and lower-bound estimates of the impact of attrition on results. LCGA inferences vary substantially depending on the handling of missing data. For older adults who die during the follow-up period, the widely used FIML approach may underestimate functional limitations by up to 20%. The most commonly used approaches to handling missing data likely underestimate the extent of poor health in aging populations. Although there is no single solution for nonrandom missingness, we show that bounding estimates can help analysts to better characterize patterns of health in later life.

Simulation evaluation of emerging estimation techniques for multinomial probit models

A simulation evaluation is presented to compare alternative estimation techniques for a five-alternative multinomial probit (MNP) model with random parameters, including cross-sectional and panel datasets and for scenarios with and without correlation among random parameters. The different estimation techniques assessed are: (1) The maximum approximate composite marginal likelihood (MACML) approach; (2) The Geweke-Hajivassiliou-Keane (GHK) simulator with Halton sequences, implemented in conjunction with the composite marginal likelihood (CML) estimation approach; (3) The GHK approach with sparse grid nodes and weights, implemented in conjunction with the composite marginal likelihood (CML) estimation approach; and (4) a Bayesian Markov Chain Monte Carlo (MCMC) approach. In addition, for comparison purposes, the GHK simulator with Halton sequences was implemented in conjunction with the traditional, full information maximum likelihood approach as well. The results indicate that the MACML approach provided the best performance in terms of the accuracy and precision of parameter recovery and estimation time for all data generation settings considered in this study. For panel data settings, the GHK approach with Halton sequences, when combined with the CML approach, provided better performance than when implemented with the full information maximum likelihood approach, albeit not better than the MACML approach. The sparse grid approach did not perform well in recovering the parameters as the dimension of integration increased, particularly so with the panel datasets. The Bayesian MCMC approach performed well in datasets without correlations among random parameters, but exhibited limitations in datasets with correlated parameters.

Northern Manhattan Hispanic Caregiver Intervention Effectiveness Study: protocol of a pragmatic randomised trial comparing the effectiveness of two established interventions for informal caregivers of persons with dementia

IntroductionThe prevalence of dementia is increasing without a known cure, resulting in an increasing number of informal caregivers. Caring for a person with dementia results in increased stress and depressive...

Is There a Credit Crunch in the Czech Republic?

We apply a disequilibrium model of credit demand and supply to test the credit crunch hypothesis. We suppose that firms face credit rationing and a realised outstanding loan will be the minimum desired level of commercial bank loans and bank limit for the firm. We adopted the disequilibrium model which consists of credit supply and credit demand equations. We suggest that actual observed credit growth rate at time t lies on the supply curve (excess demand), or on the demand curve (excess supply), or on both (equilibrium). Our model is estimated by the full-information maximum likelihood approach with a numerical maximization of the likelihood function. Our basic findings show that significant decrease in credits after the financial crisis in the year 2007 was caused by low economic and investment activity and reject the hypothesis that there is a credit crunch in the Czech Republic.

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In Search of Synergy Effects: Mergers and Productivity

We propose an alternative method for investigating whether firms improve performance through mergers after taking into account the selection bias of merging firms. We simultaneously consider the dynamics of firm performance and the merger decision by employing full information maximum likelihood (FIML) estimation. Our study differs from previous studies in that state dependence, unobservable heterogeneity, and selection bias are incorporated simultaneously. Because the effects of mergers may be felt gradually, the dynamic effects of mergers and the factors associated with these dynamics should be taken into account. Our FIML approach complements the strategy used in the extant literature for investigating the effects of mergers on firm performance.

The Effect of Protest Zeros on Estimates of Willingness to Pay in Healthcare Contingent Valuation Analysis

'Protest zeros' occur when respondents reject some aspect of the contingent valuation (CV) market scenario by reporting a zero value even though they place a positive value on the amenity being valued. This is inevitable even in the best-designed CV study, and, when excluded on an ad hoc basis, may cause a selection bias problem. This could affect the reliability of the willingness to pay (WTP) estimates obtained for preference assessment. Treatment of 'protest zeros' in general, and particularly in the context of developing countries, has been rather unsatisfactory. Most case studies employ the Heckman 2-step approach, which is much less robust to co-linearity problems than the Full Information Maximum Likelihood (FIML) estimator. The main objective of this article is to illustrate a sequential procedure to simultaneously deal with co-linearity and selectivity bias resulting from excluding 'protest zeros' in CV analysis. The sequential procedure involves different levels of estimation and diagnostics with the 2-step and FIML estimators; the duration of the procedure depends on the diagnostic test results at each stage of the estimations. The data used for the analysis were elicited using the conventional dichotomous choice buttressed with an open-ended follow-up question. The survey was designed to elicit households' WTP for a proposed community-based malaria control scheme in rural Cameroon. In the application context, we found that the different levels of estimation and diagnostics resulted in reliable WTP estimates from the FIML approach, which would obviously have been overlooked in the absence of such diagnostics.

Access to Finance and Small Enterprise Growth: Evidence from East Java

The widespread acknowledgement of the centrality of micro and small businesses in the development process has led to a proliferation of projects and programs designed to assist and promote these businesses. This research examines the common assumption that access to credit from formal financial institutions is an important determinant of growth at the firm level. Our data are from a recent survey of 858 small businesses in East Java. We employ a full information maximum likelihood approach known as discrete factor method. The results indicate that access to credit is not a significant determinant of small firm growth; instead, other observable and unobservable characteristics of firms appear to cause growth.

A Two-Stage Approach to Missing Data: Theory and Application to Auxiliary Variables

A well-known ad-hoc approach to conducting structural equation modeling with missing data is to obtain a saturated maximum likelihood (ML) estimate of the population covariance matrix and then to use this estimate in the complete data ML fitting function to obtain parameter estimates. This 2-stage (TS) approach is appealing because it minimizes a familiar function while being only marginally less efficient than the full information ML (FIML) approach. Additional advantages of the TS approach include that it allows for easy incorporation of auxiliary variables and that it is more stable in smaller samples. The main disadvantage is that the standard errors and test statistics provided by the complete data routine will not be correct. Empirical approaches to finding the right corrections for the TS approach have failed to provide unequivocal solutions. In this article, correct standard errors and test statistics for the TS approach with missing completely at random and missing at random normally distributed data are developed and studied. The new TS approach performs well in all conditions, is only marginally less efficient than the FIML approach (and is sometimes more efficient), and has good coverage. Additionally, the residual-based TS statistic outperforms the FIML test statistic in smaller samples. The TS method is thus a viable alternative to FIML, especially in small samples, and its further study is encouraged.

Estimating New-Keynesian Phillips curves: A full information maximum likelihood approach

The New-Keynesian Phillips curve has recently become an important ingredient in monetary policy models. However, using limited information methods, the empirical support for the New-Keynesian Phillips curve appear to be mixed. This paper argues, by means of Monte Carlo simulations with a simple New-Keynesian sticky price model, that single equations methods, e.g. GMM, are likely to produce imprecise and biased estimates. Then, it is argued that estimating the model with full information maximum likelihood (FIML) is a useful way of obtaining better estimates. Finally, a version of the model used in the Monte Carlo simulations is estimated on U.S. data with FIML and although the pure forward-looking New-Keynesian Phillips curve is rejected, a version with both forward- and backward-looking components provides a reasonable approximation of U.S. inflation dynamics.

The MCMC and SML estimation of a self-selection model with two outcomes

A self-selection model with discrete and continuous outcomes and a treatment variable is considered. The treatment variable is endogenous to the two outcome variables. Two estimation procedures are proposed and compared. The first estimation approach is Bayesian and uses the Markov Chain Monte Carlo (MCMC) methods. It constructs stationary Markov chains that converge to the posterior distribution of the parameters of the model. The second one is a full information maximum likelihood approach, using the simulated maximum likelihood (SML). estimator. Both methods are tested on a numerical example.

The autonomy of elasticities for trade among Canada, Japan, and the United States

This paper assembles a simultaneous model explaining trade among Canada, Japan, and the United States. Spending behaves according to the Rotterdam model which, by design, embodies all of the properties of utility maximization and does not treat trade elasticities as autonomous parameters. Pricing behaves according to the pricing-to-market hypothesis which recognizes exporters' incentives to discriminate across export markets. Parameter estimation relies on the Full Information Maximum Likelihood approach and uses bilateral price data for 1965–1987. Specifically, the estimates from the Rotterdam model predict that asymmetries in income elasticities, which were important once, have vanished.

The Autonomy of Trade Elasticities: Choice and Consequences

Fifty years of econometric work on trade assumes that trade elasticities are invariant to changes in spending patterns, that prices can be taken as given, and that expenditures on domestic and foreign goods can be studied independently of each other. To relax these assumptions, this paper assembles a simultaneous model explaining trade among Canada, Japan, and the United States. Spending behaves according to the Rotterdam model which, by design, embodies all of the properties of utility maxi­mization and does not treat trade elasticities as autonomous parameters. Pricing behaves according to the pricing-to-market hypothesis which recognizes exporters' incentives to discriminate across export markets. Parameter estimation relies on the Full Information Maximum Likelihood approach and uses bilateral price data for 1965-1987. According to the evidence, treating trade elasticities as autonomous parameters and ignoring the statistical implications of simultaneity and optimization un­dermines our effectiveness in addressing questions relevant to economic interactions among nations. Specifically, the estimates from the Rotterdam model predict that asymmetries in income elasticities, which were important once, have vanished.

FIML estimation of the dynamic simultaneous equations model with ARMA disturbances

A method is presented for the estimation of the parameters in the dynamic simultaneous equations model with vector autoregressive moving average disturbances. The estimation procedure is derived from the full information maximum likelihood approach and is based on Newton-Raphson techniques applied to the likelihood equations. The resulting two-step Newton-Raphson procedure involves only generalized instrumental variables estimation in the second step. This procedure also serves as the basis for an iterative scheme to solve the normal equations and obtain the maximum likelihood estimates of the conditional likelihood function. A nine-equation variant of the quarterly forecasting model of the US economy developed by Fair is then used as a realistic example to illustrate the estimation procedure described in the paper.