Linear Regression Diagnostics

This paper attempts to provide the user of linear multiple regression with a battery of diagnostic tools to determine which, if any, data points have high leverage or influence on the estimation process and how these possibly discrepant data points differ from the patterns set by the majority of the data. The point of view taken is that when diagnostics indicate the presence of anomolous data, the choice is open as to whether these data are in fact unusual and helpful, or possibly harmful and thus in need of modifications or deletion. The methodology developed depends on differences, derivatives, and decompositions of basic regression statistics. There is also a discussion of how these techniques can be used with robust and ridge estimators. An example is given showing the use of diagnostic methods in the estimation of a cross-country savings rate model.

The Variances of Regression Coefficient Estimates Using Aggregate Data

This paper considers the effect of aggregation on the variance of parameter estimates for a linear regression model with random coefficients and an additive error term. Aggregate and microvariances are compared and measures of relative efficiency are introduced. Necessary conditions for efficient aggregation procedures are obtained from the Theil aggregation weights and from measures of synchronization related to the work of Grunfeld and Griliches.

Area deprivation across the life course and physical capability in mid-life: findings from the 1946 British Birth Cohort

Physical capability in later life is influenced by factors occurring across the life course, yet exposures to area conditions have only been examined cross-sectionally. Data from the National Survey of Health and Development, a longitudinal study of a 1946 British birth cohort, were used to estimate associations of area deprivation (defined as percentage of employed people working in partly skilled or unskilled occupations) at ages 4, 26, and 53 years (residential addresses linked to census data in 1950, 1972, and 1999) with 3 measures of physical capability at age 53 years: grip strength, standing balance, and chair-rise time. Cross-classified multilevel models with individuals nested within areas at the 3 ages showed that models assessing a single time point underestimate total area contributions to physical capability. For balance and chair-rise performance, associations with area deprivation in midlife were robust to adjustment for individual socioeconomic position and prior area deprivation (mean change for a 1-standard-deviation increase: balance, −7.4% (95% confidence interval (CI): −12.8, −2.8); chair rise, 2.1% (95% CI: −0.1, 4.3)). In addition, area deprivation in childhood was related to balance after adjustment for childhood socioeconomic position (−5.1%, 95% CI: −8.7, −1.6). Interventions aimed at reducing midlife disparities in physical capability should target the socioeconomic environment of individuals—for standing balance, as early as childhood

Lifelong socioeconomic position and physical performance in midlife: results from the British 1946 birth cohort

Socioeconomic position (SEP) across life is found to be related to adult physical performance, but the underlying pathways are not well characterized. Using a British birth cohort (N = 2956), the associations of SEP from childhood into midlife with objective physical performance measures in midlife were examined, adjusting for possible confounders or mediators, including indicators of muscle development and central nervous system function. Childhood and adulthood SEP were positively related to standing balance and chair rise performance, but not to grip strength after basic adjustments. When both father’s occupation and mother’s education were included in the same model, having a mother with low education was associated with 0.6 standard deviations (SD) (95% confidence interval (CI: 0.3, 0.8)) poorer standing balance time compared with having a mother with the highest educational level, and having a father in the lowest occupational group was associated with a 0.3 SD (95% CI: 0.1, 0.6) lower chair rise score compared with having a father in the highest occupational group. These associations were maintained, albeit attenuated, after adjustment. In contrast, the associations of own education and adult occupation with physical performance were generally not maintained after adjustment. SEP across life impacts on midlife physical performance, and thereby the ageing process

Life course dietary patterns and bone health in later life in a British birth cohort study

Evidence for the contribution of individual foods and nutrients to bone health is weak. Few studies have considered hypothesis-based dietary patterns and bone health. We investigated whether a protein, calcium and potassium-rich (PrCaK-rich) dietary pattern over the adult life course, was positively associated with bone outcomes at 60-64 years of age. Diet diaries were collected at ages 36, 46, 53 and 60-64 years in 1263 participants (661 women) from the MRC National Survey of Health and Development. DXA and pQCT measurements were obtained at 60-64y, including size-adjusted bone mineral content (SA-BMC) and volumetric bone mineral density (vBMD). A food-based dietary pattern best explaining dietary calcium, potassium and protein intakes (g/1000?kcal) was identified using reduced rank regression. Dietary pattern z-scores were calculated for each individual, at each time point. Individual trajectories in dietary pattern z-scores were modelled to summarise changes in z-scores over the study period. Regression models examined associations between these trajectories and bone outcomes at 60-64y, adjusting for baseline dietary pattern z-score and other confounders. A consistent PrCaK-rich dietary pattern was identified within the population, over time. Mean [SD] dietary pattern z-scores at age 36 and 60-64 years were -0.32[0.97], 2.2[1.5] (women) and -0.35[0.98], 1.7[1.6] (men). Mean trajectory in dietary pattern z-scores [SD] was 0.07[0.02]SD units/year. Among women, a 0.02 SD unit/year higher trajectory in dietary pattern z-score over time was associated with higher SA-BMC (spine 1.40% [95% CI: 0.30,2.51]; hip 1.35% [95% CI: 0.48,2.23]) and vBMD (radius 1.81% [95% CI: 0.13,3.50]) at 60-64 y. No statistically significant associations were found in men. During adulthood, an increasing score for a dietary pattern rich in protein, calcium and potassium was associated with greater SA-BMC at fracture-prone sites in women. This study emphasises the importance of these nutrients, within the context of the whole diet, to bone healt

Physical and cognitive capability in mid-adulthood as determinants of retirement and extended working life in a British cohort study

OBJECTIVE: Policy in many industrialized countries increasingly emphasizes extended working life. We examined associations between physical and cognitive capability in mid-adulthood and work in late adulthood. METHODS: Using self-reported physical limitations and performance-based physical and cognitive capability at age 53, assessed by trained nurses from the Medical Research Council (MRC) National Survey of Health and Development, we examined prospective associations with extended working (captured by age at and reason for retirement from main occupation, bridge employment in paid work after retirement from the main occupation, and voluntary work participation) up to age 68 among >2000 men and women. RESULTS: Number of reported physical limitations at age 53 was associated with higher likelihood of retiring for negative reasons and lower likelihood of participating in bridge employment, adjusted for occupational class, education, partner's employment, work disability at age 53, and gender. Better performance on physical and cognitive tests was associated with greater likelihood of participating in bridge or voluntary work. Cognitive capability in the top 10% compared with the middle 80% of the distribution was associated with an odds ratio of bridge employment of 1.71 [95% confidence interval (95% CI) 1.21-2.42]. CONCLUSIONS: The possibility for an extending working life is less likely to be realized by those with poorer midlife physical or cognitive capability, independently of education, and social class. Interventions to promote capability, starting in mid-adulthood or earlier, could have long-term consequences for extending working

Work–family life course patterns and work participation in later life

Many developed nations seek to increase older people’s work participation. Work and family are linked to paid work in later life, and to each other. Few studies combined work and family histories using multichannel sequence analysis capturing status and timing of transitions in relation to work in later life. Using the MRC National Survey of Health and Development, for whom State Pension Age was age 65 (men) or 60 (women), we examined paid work at age 60–64 (and age 68–69 for men only) by work–family patterns across 35 years (ages 16–51). Women’s later work was related to the combination of timing of children and work during family formation. Women who had children later were more likely to work full-time at age 60–64 compared to the reference [characterised by continuous full-time employment, marriage, and children from their early 20s; adjusted OR 5.36 (95% CI 1.84, 15.60)]. Earlier motherhood was associated with lower likelihood of work at age 60–64 among those who did not return to work before age 51, but those who took a work break did not differ from those who worked continuously. Providing jobs which allow parents to combine work and family (e.g. part-time jobs) may encourage them to extend their working lives. In addition, men and women characterised by continuous full-time work and no children were less likely to work in their sixties. Associations were not explained by childhood health and social class, education, caregiving, housing tenure, or limiting illness. Research is needed to understand why childless people work less in later life

Using Super-Imposition by Translation And Rotation (SITAR) to relate pubertal growth to bone health in later life:the Medical Research Council (MRC) National Survey of Health and Development

BACKGROUND: To explore associations between pubertal growth and later bone health in a cohort with infrequent measurements, using another cohort with more frequent measurements to support the modelling, data from the Medical Research Council (MRC) National Survey of Health and Development (2-26 years, 4901/30 004 subjects/measurements) and the Avon Longitudinal Study of Parents And Children (ALSPAC) (5-20 years) (10 896/74 120) were related to National Survey of Health and Development (NSHD) bone health outcomes at 60-64 years. METHODS: NSHD data were analysed using Super-Imposition by Translation And Rotation (SITAR) growth curve analysis, either alone or jointly with ALSPAC data. Improved estimation of pubertal growth parameters of size, tempo and velocity was assessed by changes in model fit and correlations with contemporary measures of pubertal timing. Bone outcomes of radius [trabecular volumetric bone mineral density (vBMD) and diaphysis cross-sectional area (CSA)] were regressed on the SITAR parameters, adjusted for current body size. RESULTS: The NSHD SITAR parameters were better estimated in conjunction with ALSPAC, i.e. more strongly correlated with pubertal timing. Trabecular vBMD was associated with early height tempo, whereas diaphysis CSA was related to weight size, early tempo and slow velocity, the bone outcomes being around 15% higher for the better vs worse growth pattern. CONCLUSIONS: By pooling NSHD and ALSPAC data, SITAR more accurately summarized pubertal growth and weight gain in NSHD, and in turn demonstrated notable associations between pubertal timing and later bone outcomes. These associations give insight into the importance of the pubertal period for future skeletal health and osteoporosis risk

Students as co-creators of teaching approaches, course design and curricula: implications for academic developers

Within higher education, students’ voices are frequently overlooked in the design of teaching approaches, courses and curricula. In this paper we outline the theoretical background to arguments for including students as partners in pedagogical planning processes. We present examples where students have worked collaboratively in design processes along with the beneficial outcomes of these examples. Finally we focus on some of the implications and opportunities for academic developers of proposing collaborative approaches to pedagogical planning