An extension of the mixed-effects growth model that considers between-person differences in the within-subject variance and the autocorrelation.

Experience sampling methods have led to a significant increase in the availability of intensive longitudinal data. Typically, this type of data is analyzed with a mixed-effects model that allows to examine hypotheses concerning between-person differences in the mean structure by including multiple random effects per individual (eg, random intercept and random slopes). Here, we describe an extension of this model that-in addition to the random effects for the mean structure-also includes a random effect for the within-subject variance and a random effect for the autocorrelation. After the description of the model, we show how its parameters can be efficiently estimated using a marginal maximum likelihood (ML) approach. We then illustrate the model using a real data example. We also present the results of a small simulation study in which we compare the ML approach with a Bayesian estimation approach.

Putting the individual into reliability: Bayesian testing of homogeneous within-person variance in hierarchical models.

Measurement reliability is a fundamental concept in psychology. It is traditionally considered a stable property of a questionnaire, measurement device, or experimental task. Although intraclass correlation coefficients (ICC) are often used to assess reliability in repeated measure designs, their descriptive nature depends upon the assumption of a common within-person variance. This work focuses on the presumption that each individual is adequately described by the average within-person variance in hierarchical models. And thus whether reliability generalizes to the individual level, which leads directly into the notion of individually varying ICCs. In particular, we introduce a novel approach, using the Bayes factor, wherein a researcher can directly test for homogeneous within-person variance in hierarchical models. Additionally, we introduce a membership model that allows for classifying which (and how many) individuals belong to the common variance model. The utility of our methodology is demonstrated on cognitive inhibition tasks. We find that heterogeneous within-person variance is a defining feature of these tasks, and in one case, the ratio between the largest to smallest within-person variance exceeded 20. This translates into a tenfold difference in person-specific reliability! We also find that few individuals belong to the common variance model, and thus traditional reliability indices are potentially masking important individual variation. We discuss the implications of our findings and possible future directions. The methods are implemented in the R package vICC.

Performance of statistical methods to correct food intake distribution: comparison between observed and estimated usual intake.

There are statistical methods that remove the within-person random error and estimate the usual intake when there is a second 24-h recall (24HR) for at least a subsample of the study population. We aimed to compare the distribution of usual food intake estimated by statistical models with the distribution of observed usual intake. A total of 302 individuals from Rio de Janeiro (Brazil) answered twenty, non-consecutive 24HR; the average length of follow-up was 3 months. The usual food intake was considered as the average of the 20 collection days of food intake. Using data sets with a pair of 2 collection days, usual percentiles of intake of the selected foods using two methods were estimated (National Cancer Institute (NCI) method and Multiple Source Method (MSM)). These estimates were compared with the percentiles of the observed usual intake. Selected foods comprised a range of parameter distributions: skewness, percentage of zero intakes and within- and between-person intakes. Both methods performed well but failed in some situations. In most cases, NCI and MSM produced similar percentiles between each other and values very close to the true intake, and they better represented the usual intake compared with 2-d mean. The smallest precision was observed in the upper tail of the distribution. In spite of the underestimation and overestimation of percentiles of intake, from a public health standpoint, these biases appear not to be of major concern.

Estimation of the salt intake distribution of Dutch kidney transplant recipients using 24-h urinary sodium excretion: the potential of external within-person variance.

BACKGROUND: There is growing interest in assessing a population's prevalence of inadequate nutrient intake using biomarkers. However, within-person variation is generally ignored because repeated data collections are considered costly and burdensome. OBJECTIVES: The study aimed to show the importance of estimating, from repeated 24-h urine collections, a population's habitual salt intake and to explore the potential of using the ratio of within-person variance to total variance from an external source (W:T variance) with single 24-h urine collection. METHODS: Salt intake was predicted from data for 24-h urinary sodium excretion in adult kidney transplant recipients in 1992-1997 (n = 432) and 2006-2011 (n = 1159). The salt intake distribution of single-day measurements was compared with estimates from multiple 24-h urine collections, which were statistically corrected for within-person variance. Habitual salt intake was also estimated using single-day measurements and external variance estimates. From each distribution, the proportion below specified cut-off values was estimated. RESULTS: In 2006-2011 the average habitual salt intake was 10.6 g/d (men) and 8.5 g/d (women); in 1992-1997 these values were 8.6 g/d and 7.5 g/d, respectively. The proportion with salt intake <6 g/d was 5% and 13% in 2006-2011 and 22% and 28% in 1992-1997, respectively, for men and women. Correction for within-person variance significantly narrowed the salt intake distribution-the proportion with salt intake <6 g/d was overestimated by 3-13 percentage points using single-day data. Sensitivity analyses showed the importance of a sufficient sample size for estimating variance components. Variation of the W:T variance showed up to 40 percentage points deviation in the proportion with intakes below a specified cut-off value. CONCLUSIONS: To estimate a population's salt intake distribution, it is important to correct 24-h urinary sodium excretion for within-person variance. Predicting habitual salt intake distribution using single-day measurements with external variances is promising; a sensitivity analysis is recommended to show the effect of different external variances.

Examining Population Differences in Within-Person Variability in Longitudinal Designs Using Latent Variable Modeling: An Application to the Study of Cognitive Functioning of Older Adults.

Longitudinal studies have steadily grown in popularity across the educational and behavioral sciences, particularly with the increased availability of technological devices that allow the easy collection of repeated measures on multiple dimensions of substantive relevance. This article discusses a procedure that can be used to evaluate population differences in within-person (intraindividual) variability in such longitudinal investigations. The method is based on an application of the latent variable modeling methodology within a two-level modeling framework. The approach is used to obtain point and interval estimates of the differences in within-person variance and in the strength of correlative effects of repeated measures between normal and very mildly demented persons in a longitudinal study of a diagnostic cognitive test assessing verbal episodic memory.

Change in Australian Vitamin A Intakes over Time.

BACKGROUND: The mean intake of vitamin A of Australians aged 2 y and older was 300 µg retinol equivalents lower in the 2011-2012 national nutrition survey than in 1995 and decreases preponderated in adults rather than young children. OBJECTIVE: This aim of this study was to identify the foods associated with this change and to examine how the method used to adjust for within-person variability affects the estimated prevalence of inadequate intakes in both surveys. METHODS: Foods contributing to vitamin A intake were calculated from the first day of data. The prevalence of inadequate intakes was calculated using a 2-d average, the Iowa State University method, and the National Cancer Institute (NCI) method and either taken from the published reports or calculated using Food Standards Australia New Zealand's in-house software. RESULTS: In adults, lower consumption of liver, yellow fat spreads, milk products, and carrots and similar root vegetables accounted for most of the change in intake. Vitamin A intake data were less right-skewed in 2011-2012 than in 1995. The prevalence of inadequate vitamin A intake depended on the adjustment method chosen: for example, in 2011-2012 it ranged between 3% and 55% in men aged 19-30 y. The NCI method prevalence (21% for this group) is taken as the preferred estimate of inadequacy because the method adjusts around the mean and accounts for several other sources of variance. However, the NCI method could not be used to analyze the 1995 survey. CONCLUSIONS: The lower vitamin A intake in Australia was related to changes in retinol intake rather than carotenoid intake and to lower consumption of several different types of food. The estimated prevalence of inadequate intake depends on the statistical method chosen for analysis. A direct measure of vitamin A status is needed to allow conclusions about the implications of the decreasing intake of this vitamin.

Variância intrapessoal para ajuste da distribuição de nutrientes em estudos epidemiológicos / Within-person variance for adjusting nutrient distribution in epidemiological studies / Varianza intrapersonal para ajuste de la distribución de nutrientes en estudios epidemiológicos

O objetivo do estudo foi apresentar a fração da variância intrapessoal para ajuste da distribuição de nutrientes de adultos e idosos. Utilizaram-se dados de inquérito populacional com amostra representativa (n = 511) de indivíduos com 19 anos ou mais do município de São Paulo, SP, em 2007. A fração da variância intrapessoal foi obtida pelo método proposto pela Iowa State University. Observaram-se diferenças nas frações das variâncias intrapessoais de nutrientes segundo sexo. Esses valores devem ser utilizados para ajustar a distribuição da ingestão de nutrientes, pois sua não utilização pode resultar em viés na análise e interpretação de dados.

The objective of the study was to present the within-person variance component for adjusting nutrient distribution in adults and elderly people. The data used were from a population-based survey with a representative sample (n = 511) of individuals aged 19 years and over in the municipality of São Paulo, Southeastern Brazil, conducted in 2007. The within-person variance component was obtained using the Iowa State University method. Differences in within-person variance components were observed for some nutrients according to gender. These values should be used to adjust nutrient intake distributions, because lack of adjustment may result in biased data analysis and interpretation.

El objetivo del estudio fue presentar la fracción de la varianza intrapersonal para juste de la distribución de nutrientes de adultos y ancianos. Se utilizaron datos de pesquisa poblacional con muestra representativa de 511 individuos con 19 años o más del municipio de Sao Paulo, Sureste de Brasil, en 2007. La fracción de la varianza intrapersonal fue obtenida por el método propuesto por el Iowa State University. Se observaron diferencias en las fracciones de las varianzas intrapersonales de nutrientes según género. Estos valores deben ser utilizados para ajustar la distribución de la ingestión de nutrientes, ya que la no utilización puede resultar en sesgo en el análisis e interpretación de datos.