Maximum Likelihood Imputation Research Articles

The efficiency of multiple imputation and maximum likelihood methods for estimating missing values

Objectives: This study investigated the efficiency of Multiple Imputation (MI) and Maximum Likelihood (ML) methods for estimating missing values. The study was set to use the findings to make recommendations for future studies about the impact of missing data imputation on the accuracy of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). Methods: The completedset (with no missing values) used in this study was collected in 2010/11 through the Income and Expenditure Survey (IES) and had 25328 observations. Missing data were generated by randomly deleting 10%, 20%, 30%, 40% and 50% of the values from the complete dataset. The missing values in each of the five datasets were imputed using MI and ML methods. Subsequently, absolute error values of AIC and BIC from multiple regression analysis were computed for each dataset. The study then compared the absolute errors for each missing value imputation method. Findings: The findings of the study revealed that AIC and BIC are more accurate when missing values are estimated by the Full Information Maximum Likelihood (FIML) of the ML algorithm, provided 10% of the data are missing. For all datasets, AIC and BIC were least accurate when missing values were imputed by Expectation Maximisation (EM) of the ML algorithm. The findings also showed that AIC and BIC are more accurate when the rate of MISSINGNESS gets large provided missing values were estimated using either the Fully Conditional Specification (FCS) or Markov Chain Monte Carlo (MCMC), MI algorithms. Application: When the rate of MISSINGNESS is small (at most 10%), FIML should be used to handle missing data if AIC and BIC are going to be used. Also both FCS and MCMC should be considered over EM algorithms when the rate of MISSINGNESS is high (at least 40% missing). Keywords: Maximum Likelihood Imputation, Multiple Imputation, AIC, BIC

An implementation trial of ACT-based bibliotherapy for irritable bowel syndrome

BackgroundIrritable Bowel Syndrome is a gastrointestinal disorder that is associated with pain, discomfort, constipation and diarrhoea. It affects around 20% of adults in Western countries. Reports of distress and self-consciousness, as well as experiential and situational avoidance are common. Previous studies have shown that ACT may be effective for people with IBS. MethodsAn uncontrolled trial of ACT based bibliotherapy was undertaken in a specialist motility clinic. Outcomes were measured with standardised self-report questionnaires pre-treatment, and at two and six months. Missing data was handled using maximum likelihood imputation. Data was analysed using repeated measures ANOVA. Results45 participants enrolled in the study, with 36 providing data at two months, and 24 at six months. Participants were predominantly female, with an average ten-year history of IBS, and 71% of the sample had moderate or severe symptoms. At six months,participants had improved on symptom severity (ηp2=.09, 90% CI=.01−.18), GI specific anxiety (ηp2=.07, 90% CI=.01−.16) and IBS willingness (ηp2=.14, 90% CI=.04−.24), but had not shown behavioural changes towards greater activity, (ηp2=.01, 90% CI=.0−.05) or to reduce IBS avoidance behaviours (ηp2=.05, 90% CI=.0=.13). Contrary to hypothesis, intervention did not reduce the impact of IBS on quality of life(ηp2=.04, 90% CI=.0−.09). DiscussionBibliotherapy interventions may be useful for people with refractory IBS, though greater contact and structured exposure may be necessary to change behaviour. The study was limited by problems with attrition, though these data suggest future research in this area would be worthwhile.

The Bias and Efficiency of Incomplete-Data Estimators in Small Univariate Normal Samples

Widely used methods for analyzing missing data can be biased in small samples. To understand these biases, we evaluate in detail the situation where a small univariate normal sample, with values missing at random, is analyzed using either observed-data maximum likelihood (ML) or multiple imputation (MI). We evaluate two types of MI: the usual Bayesian approach, which we call posterior draw (PD) imputation, and a little used alternative, which we call ML imputation, in which values are imputed conditionally on an ML estimate. We find that observed-data ML is more efficient and has lower mean squared error than either type of MI. Between the two types of MI, ML imputation is more efficient than PD imputation, and ML imputation also has less potential for bias in small samples. The bias and efficiency of PD imputation can be improved by a change of prior.

Handling missing data in self-report measures

Self-report measures are extensively used in nursing research. Data derived from such reports can be compromised by the problem of missing data. To help ensure accurate parameter estimates and valid research results, the problem of missing data needs to be appropriately addressed. However, a review of nursing research literature revealed that issues such as the extent and pattern of missingness, and the approach used to handle missing data are seldom reported. The purpose of this article is to provide researchers with a conceptual overview of the issues associated with missing data, procedures used in determining the pattern of missingness, and techniques for handling missing data. The article also highlights the advantages and disadvantages of these techniques, and makes distinctions between data that are missing at the item versus variable levels. Missing data handling techniques addressed in this article include deletion approaches, mean substitution, regression-based imputation, hot-deck imputation, multiple imputation, and maximum likelihood imputation.