Scott M. Hofer

Maximizing the Usefulness of Data Obtained with Planned Missing Value Patterns: An Application of Maximum Likelihood Procedures

Researchers often face a dilemma: Should they collect little data and emphasize quality, or much data at the expense of quality? The utility of the 3-form design coupled with maximum likelihood methods for estimation of missing values was evaluated. In 3-form design surveys, four sets of items. X, A, B, and C are administered: Each third of the subjects receives X and one combination of two other item sets - AB, BC, or AC. Variances and covariances were estimated with pairwise deletion, mean replacement, single imputation, multiple imputation, raw data maximum likelihood, multiple-group covariance structure modeling, and Expectation-Maximization (EM) algorithm estimation. The simulation demonstrated that maximum likelihood estimation and multiple imputation methods produce the most efficient and least biased estimates of variances and covariances for normally distributed and slightly skewed data when data are missing completely at random (MCAR). Pairwise deletion provided equally unbiased estimates but was less efficient than ML procedures. Further simulation results demonstrated that nun-maximum likelihood methods break down when data are not missing completely at random. Application of these methods with empirical drug use data resulted in similar covariance matrices for pairwise and EM estimation, however, ML estimation produced better and more efficient regression estimates. Maximum likelihood estimation or multiple imputation procedures. which are now becoming more readily available, are always recommended. In order to maximize the efficiency of the ML parameter estimates, it is recommended that scale items be split across forms rather than being left intact within forms.

Analysis with missing data in prevention research

Missing data problems have been a thorn in the side of prevention researchers for years. Although some solutions for these problems have been available in the statistical literature, these solutions have not found their way into mainstream prevention research. This chapter is meant to serve as an introduction to the systematic application of the missing data analysis solutions presented recently by Little and Rubin (1987) and others. The chapter does not describe a complete strategy, but it is relevant for (1) missing data analysis with continuous (but not categorical) data, (2) data that are reasonably normally distributed, and (3) solutions for missing data problems for analyses related to the general linear model in particular, analyses that use (or can use) a covariance matrix as input. The examples in the chapter come from drug prevention research. The chapter discusses (1) the problem of wanting to ask respondents more questions than most individuals can answer; (2) the problem of attrition and some solutions; and (3) the problem of special measurement procedures that are too expensive or time consuming to obtain for all subjects. The authors end with several conclusions: Whenever possible, researchers should use the Expectation-Maximization (EM) algorithm (or other maximum likelihood procedure, including the multiple-group structural equation-modeling procedure or, where appropriate, multiple imputation, for analyses involving missing data [the chapter provides concrete examples]); If researchers must use other analyses, they should keep in mind that these others produce biased results and should not be relied upon for final analyses; When data are missing, the appropriate missing data analysis procedures do not generate something out of nothing but do make the most out of the data available; When data are missing, researchers should work hard (especially when planning a study) to find the cause of missingness and include the cause in the analysis models; and Researchers should sample the cases originally missing (whenever possible) and adjust EM algorithm parameter estimates accordingly.

Understanding Ageing. An evaluation of research designs for assessing the interdependence of ageing-related changes.

Background: Cross-sectional studies of samples varying widely in age have found moderate to high levels of shared age-related variance among measures of cognitive and physiological capabilities, leading researchers to posit common factors or common causal influences for diverse age-related phenomenon. Objective: The influence of population average changes with age on cross-sectional estimates of association has not been widely appreciated in developmental and ageing research. Covariances among age-related variables in cross-sectional studies are highly confounded in regards to inferences about associations among rates of change within individuals since covariances can result from a number of sources including average population age-related differences (fixed age effects) in addition to initial individual differences and individual differences in rates of ageing (random age effects). Analysis of narrow age-cohort samples may provide a superior analytical basis for testing hypotheses regarding associations between rates of change in cross-sectional studies. Conclusions: The use of age-heterogeneous cross-sectional designs for evaluating interdependence of ageing-related processes is discouraged since associations will not necessarily reflect individual-level correlated rates of change. Typical cross-sectional studies do not provide sufficient evidence for the interdependence of ageing-related changes and should not serve as the basis for theories and hypotheses of ageing. Reanalyzing existing cross-sectional studies using a sequential narrow-age cohort approach provides a useful alternative for evaluating associations between ageing-related changes. Longitudinal designs, however, provide a much stronger basis for inference regarding associations between rates of ageing within individuals.

Intraindividual coupling of daily stress and cognition.

Most psychological theories predict associations among processes that transpire within individuals. However, these theories are often tested by examining relationships at the between-persons (BP) rather than the within-persons (WP) level. The authors examined the WP and BP relationships between daily stress and daily variability in cognitive performance. Daily stress and cognitive performance were assessed on 6 occasions in 108 older adults and 68 young adults. WP variability in stress predicted WP variability in response times (RTs) on a 2-back working memory task in both younger and older adults. That is, RTs were slower on high-stress days compared with low-stress days. There was evidence of an amplified WP stress effect in the older adults on a serial attention task. There was no evidence of stress effects on simple versions of these tasks that placed minimal demands on working memory. These results are consistent with theories that postulate that stress-related cognitive interference competes for attentional resources.

Type 2 diabetes mellitus contributes to cognitive decline in old age: A longitudinal population-based study

We examined change in neuropsychological test performance related to type 2 diabetes mellitus across a 6-year interval. A population-based sample of 274 elderly participants (36 with diabetes and 238 without diabetes) was examined at four occasions at a 2-year interval. The participants were 80-93 years of age (M = 82.8 years) and without dementia at baseline. The test battery included tests of speed, visuospatial ability, short-term memory, semantic memory, episodic memory, and the Mini Mental Status Examination. Several models, taking into account diabetes and demographic data, were analyzed using SAS Proc Mixed multilevel modeling. At baseline, there were no significant differences in the neuropsychological tests related to diabetes. The longitudinal analyses, however, showed that diabetes was a significant predictor of decline for many of the tests. These findings points to the conclusion that type 2 diabetes is associated with accelerated cognitive decline in old age that may result in dementia.

A Latent Growth Curve Analysis of Late-Life Sensory and Cognitive Function over 8 Years: Evidence for Specific and Common Factors Underlying Change

Correlations among rates of change in sensory and cognitive functioning in adulthood were evaluated. Measures of Vision, Hearing, Memory, Speed and Verbal ability were obtained in 1992, 1994, and 2000 in the Australian Longitudinal Study of Aging (N = 2,087 at baseline). Data from 1,823 participants who undertook at least 1 clinical assessment were analyzed using latent growth curve models. A significant moderate-sized association between rates of change in Memory and Vision was found. This remained after statistically controlling for the effects of age, gender, education, self-rated health, medical conditions, and depressive symptoms. Rate of change in Hearing was weakly associated with rate of change in Memory. The results support a theory incorporating a major role for unique factors in addition to common factors underlying sensory and cognitive change in old age.

The Dynamic Relationship Between Physical Function and Cognition in Longitudinal Aging Cohorts

On average, older people remember less and walk more slowly than do younger persons. Some researchers argue that this is due in part to a common biologic process underlying age-related declines in both physical and cognitive functioning. Only recently have longitudinal data become available for analyzing this claim. We conducted a systematic review of English-language research published between 2000 and 2011 to evaluate the relations between rates of change in physical and cognitive functioning in older cohorts. Physical functioning was assessed using objective measures: walking speed, grip strength, chair rise time, flamingo stand time, and summary measures of physical functioning. Cognition was measured using mental state examinations, fluid cognition, and diagnosis of impairment. Results depended on measurement type: Change in grip strength was more strongly correlated with mental state, while change in walking speed was more strongly correlated with change in fluid cognition. Examining physical and cognitive functioning can help clinicians and researchers to better identify individuals and groups that are aging differently and at different rates. In future research, investigators should consider the importance of identifying different patterns and rates of decline, examine relations between more diverse types of measures, and analyze the order in which age-related declines occur.

Modeling Memory Decline in Older Adults: The Importance of Preclinical Dementia, Attrition, and Chronological Age

This longitudinal study examined memory loss in a sample of 391 initially nondemented older adults. Analyses decomposed observed memory loss into decline associated with preclinical dementia, study attrition, terminal decline, and chronological age. Measuring memory as a function of only chronological age failed to provide an adequate representation of cognitive change. Disease progression accounted for virtually all of the memory loss in the 25% of the sample that developed diagnosable dementia. In the remainder of the sample, both chronological age and study attrition contributed to observed memory loss. These results suggest that much of memory loss in aging adults may be attributable to the progression of preclinical dementia and other nonnormative aging processes that are not captured by chronological age.

Evaluating the Interdependence of Aging-Related Changes in Visual and Auditory Acuity, Balance, and Cognitive Functioning

High proportions of shared age-related variance are found among measures of perceptual acuity, balance, muscle strength, and cognitive capabilities in age-heterogeneous, cross-sectional studies. Reliance on cross-sectional studies is problematic, however, because associations may arise from age-related mean trends. Narrow age-cohort samples provide an alternative basis for testing hypotheses regarding associations among rates of change. Cross-domain associations were evaluated in combined 75-year-old cohort samples from Denmark, Finland, and Sweden. In general, no consistent associations were found across sensory, balance, strength, and cognitive domains. These findings indicate that the effects of aging on sensory acuity, balance, and cognitive functioning are likely to be largely independent, multidimensional, and complex at the level of the individual.

Cross-sectional and Longitudinal Patterns of Dedifferentiation in Late-life Cognitive and Sensory Function: The Effects of Age, Ability, Attrition, and Occasion of Measurement

The dedifferentiation hypothesis is examined with respect to age-group differences, ability-group differences, attrition-group differences, and time. Cognitive and sensory data were analyzed from individuals (n = 1,823) who completed a clinical assessment on at least 1 of 3 occasions of measurement in the Australian Longitudinal Study of Ageing. Inconsistent dedifferentiation effects were associated with low ability and early attrition from the study, but age-related dedifferentiation was not found. Longitudinal analyses confirmed the cross-sectional analyses. Even though instances of dedifferentiation were identified between pairs of sensory and cognitive variables, consistent patterns of dedifferentiation were not found. These results do not support the view that shared biological factors become increasingly important for explaining within-individual change in cognitive and sensory function in later life.