From Noise to Signal: The Age and Social Patterning of Intra-Individual Variability in Late-Life Health

Abstract

Objectives.

Despite a long tradition of attending to issues of intra-individual variability in the gerontological literature, large-scale panel studies on late-life health disparities have primarily relied on average health trajectories, relegating intra-individual variability over time to random error terms, or “noise.” This article reintegrates the systematic study of intra-individual variability back into standard growth curve modeling and investigates the age and social patterning of intra-individual variability in health trajectories.

Method.

Using panel data from the Health and Retirement Study, we estimate multilevel growth curves of functional limitations and cognitive impairment and examine whether intra-individual variability in these two health outcomes varies by age, gender, race/ethnicity, and socioeconomic status, using level-1 residuals extracted from the adjusted growth curve models.

Results.

For both outcomes, intra-individual variability increases with age. Racial/ethnic minorities and individuals with lower socioeconomic status tend to have greater intra-individual variability in health. Relying exclusively on average health trajectories may have masked important “signals” of life course health inequality.

Discussion.

The findings contribute to scientific understanding of the source of heterogeneity in late-life health and highlight the need to further investigate specific life course mechanisms that generate the social patterning of intra-individual variability in health status.

In their influential discussion of successful aging, Rowe and Kahn (1997) proposed that intra-individual variability in health should be considered as a critical dimension for aging research. This was based predominately on a growing body of literature that reported increasing intra-individual variability in physiological and cognitive outcomes at upper ages, often as a precursor of end-of-life processes and mortality (e.g., Eizenman, Nesselroade, Featherman, & Rowe, 1997; Kim, Nesselroade, & Featherman, 1996).

Accordingly, a stream of gerontological studies has focused on how fluctuations over time within individuals can be meaningfully related to chronological age. Upon review, studies consistently show that intra-individual variability increases systematically with age across a number of functional indicators. For example, greater fluctuations in mobility disability (Gill, Allore, Hardy, & Guo, 2006) and in gait (Callisaya, Blizzard, Schmidt, McGinley, & Srikanth, 2010) are more commonly observed among adults aged 70 and older, which is attributed to fluctuations in symptoms and severity of the conditions that affect physical function in later life (Campbell & Buchner, 1997; Gill et al., 2006). A rich body of literature has examined age-associated fluctuations in various indicators of cognition. Adults aged 60 and older are found to be less stable in reaction time (Hultsch, MacDonald, & Dixon, 2002) and executive control (West, Murphy, Armilio, Craik, & Stuss, 2002) than are younger adults. There is a continuous age-based increase in intra-individual variability in cognitive performance in young-old (aged 50 and older; Hultsch, MacDonald, Hunter, Levy-Bencheton, & Strauss, 2000; Li, Aggen, Nesselroade, & Baltes, 2001; MacDonald, Hultsch, & Dixon, 2003) and old-old samples (aged 80 and older; Ram, Gerstorf, Lindenberger, & Smith, 2011). In addition, two longitudinal studies found increasing intra-individual variability in cognition with age throughout adulthood (Bielak, Cherbuin, Bunce, & Anstey, 2014; Fozard, Vercruyssen, Reynolds, Hancock, & Quilter, 1994).

Some work in this line of inquiry has taken the next step to identify whether there are differences in patterns of intra-individual variability between socially meaningful subgroups, such as gender, race, and socioeconomic status. Even after accounting for age and comorbidity, women are found to be more variable than men in walking stability (Callisaya et al., 2010), mental health (Hauck & Rice, 2004), and cognitive speed (Bielak et al., 2014). Greater fluctuations in self-rated health are observed among racial/ethnic minorities (Contoyannis, Jones & Rice, 2004) and those with non-English speaking backgrounds (Christensen et al., 2005). Two studies found that higher levels of education and income were associated with greater fluctuations in self-rated health (Contoyannis et al., 2004; Hauck & Rice, 2004), whereas Christensen and colleagues (2005) found exactly the opposite for cognitive impairment: Individuals with more education tended to be less variable.

Despite these valuable discoveries, it is surprising that inquiry about intra-individual variability has not been fully integrated into large-scale panel studies. With the rapidly expanding use of trajectory modeling, often only the average health trajectory is of central analytic and substantive concern (e.g., Alley, Suthers, & Crimmins, 2007; Brown, O’Rand, & Adkins, 2012; Herd, 2006; Liang et al., 2005; Shuey & Willson, 2008; Spence, Adkins, & Dupre, 2011; Yang & Lee, 2009). An unintended consequence of the typical application of trajectory modeling is that intra-individual variability over time, that is, the deviation of each panel assessment from individual mean, is relegated to random errors, or “noise,” around the averaged individual trajectories (Kelley-Moore & Lin, 2011; Singer & Willett, 2003). As a result, many studies characterize observed fluctuations in health outcomes as “random error” (Liang et al., 2005), “random within-person error” (Yang & Lee, 2009), “within-individual residual” (Spence et al., 2011), or “model residual” (Brown et al., 2012), without recognizing them as a theoretically interesting and substantively important aspect of health and aging.

In this study, we focus on intra-individual variability over an extended period of time in late-life functional limitations and cognitive impairment, both of which are important domains of well-being in older adulthood. We begin by exploring whether there is any systematic age patterning to intra-individual variability in these two domains or whether the fluctuations over time are just random noise. If systematic patterning does exist, it then directly challenges the typical application of trajectory modeling which tends to “smooth” variations between measurement occasions and characterize change as its average rate over time. Next, we consider the degree to which social factors influence intra-individual variability in physical and cognitive functioning. Unlike other psychosocial domains such as life satisfaction and social support, intra-individual variability in functioning may feed into aging stereotypes, such as diminished stability at upper ages, when its social patterns are not taken into consideration.

Although pursuing the specific mechanisms that drive intra-individual variability in a given health indicator to increase with age and to become greater for certain groups is important in its own right (see Martin & Hofer, 2004 and Nesselroade & Salthouse, 2004), we aim to demonstrate how patterns of long-term intra-individual variability (i.e., within-persons) could enrich theoretical and empirical work on life course inter-individual (i.e., between-persons) variability in two ways. First, although studies have documented increasing intracohort heterogeneity with age in health using large-scale panel data (e.g., Mirowsky & Ross, 2008; Shuey & Willson, 2008), the question of whether such a phenomenon is largely driven by intra-individual or inter-individual processes has not been subject to close study. At the cohort level, an overall tendency for intracohort heterogeneity to increase over time may conceivably result from several distinct kinds of empirically measurable processes, including inter-individual divergence as proposed in cumulative dis/advantage theory (Dannefer, 2003), increasing intra-individual variability with age (Baltes, 1979), or some combination of both. To date, it remains unclear whether intra-individual variability increases systematically with age for a birth cohort, which would in turn contribute to or even account for some heterogeneity that was previously attributed to between-individual processes. Panel data are ideal for disentangling drivers of age-based patterns of heterogeneity, and such work will be important to testing life course theories that are concerned with cohort-level heterogeneity, particularly cumulative dis/advantage theory.

Second, we present a novel conceptual perspective that complements extant explanatory frameworks of intra-individual variability, which have to date focused predominantly on its nonsocial sources, such as compromised neurobiological systems (e.g., West et al., 2002) and psychological resilience (e.g., Ram et al., 2011). Explanations to increasing intra-individual variability with age, in particular, have been drawn from frameworks that attribute such changes to normative aging (e.g., Baltes, 1979; Bielak et al., 2014). Also called an instability hypothesis, such a perspective posits that increasing variability results from reduction in stability with advancing age. When intra-individual variability is relegated to “noise,” the plausibility of the instability hypothesis remains unexamined and any alternative hypothesis on the sociogenic causes of intra-individual variability is not tested.

Is intra-individual variability merely random “noise” caused by physiological instability, or the “signal” of a new frontier for theorizing novel sociostructural explanations to life course health inequality? To answer this question, we undertake a systematic study of long-term intra-individual variability in health trajectories within a growth curve modeling framework. Using panel data collected biannually from the Health and Retirement Study (HRS), we address two specific research questions. First, does intra-individual variability in functional limitations and cognitive impairment change systematically with age and if so, what are these age-based patterns? Intra-individual variability may increase, decrease, fluctuate, or remain stable with age for different health domains (Figure 1). For functional limitations and cognitive impairment, we hypothesize that intra-individual variability increases with age because reduction in physiological capacity at upper ages makes one’s functioning more sensitive to social environmental influences, thereby increasing fluctuations over time (Campbell & Buchner, 1997).

Figure 1.

Hypothesized age-based patterns of intra-individual variability in health.

Second, does intra-individual variability in functional limitations and cognitive impairment vary by social factors such as gender, race/ethnicity, and socioeconomic status? Because a host of social factors, particularly gender, race/ethnicity, and socioeconomic status, all strongly affect late-life health and functioning, we further hypothesize that a considerable amount of intra-individual variability can be attributed to one’s social position, which determines, for example, whether he/she has stable employment and income, as well as regular access to health care and support. If intra-individual variability in health is socially organized instead of being random noise, a sociostructural explanation to such variability—other than instability with advancing age—is warranted.

Method

Data and Sample

We employ eight waves (1996/Wave 3 to 2010/Wave 10) of panel data from the HRS, which is an ongoing panel study of a nationally representative sample of adults aged 51 and older interviewed every 2 years from 1992. The HRS utilizes a multistage area probability sampling design and has oversamples of Black and Hispanic adults, allowing us to adequately examine racial/ethnic patterns in intra-individual variability.

The analytic sample is limited to the HRS cohort (born 1931–1941) to eliminate potential cohort variations in study variables. Only non-Hispanic White, non-Hispanic Black, and Hispanic respondents are included, because there are too few respondents in other racial/ethnic categories to permit meaningful analysis. After excluding proxy interviews, we further limit the analysis to individuals who have at least two observation points to allow an examination of variability within individuals. Separate analytic data sets are made for functional limitations (n = 7,715 individuals; 43,680 observations; Wave 3 to Wave 10) and cognitive impairment (n = 6,985 individuals; 29,944 observations; Wave 3 to Wave 9) to increase sample size for each outcome.

Measures

Outcomes

There are two outcome variables—functional limitations and cognitive impairment. Functional limitations are measured with 11 limitations related to mobility, strength, and upper- and lower-body tasks (e.g., walking several blocks, raising arms above the shoulder; Wallace & Herzog, 1995). Respondents indicated how much difficulty they had when performing each task on the following scale: no difficulties (=0), some difficulties (=1), and a lot of difficulties (=2). A composite measure is created as the sum score of all 11 limitations, ranging from 0 to 22. For the young-old population in the HRS, this scale measures their physical function more precisely than the standard activities of daily living and instrumental activities of daily living assessments, which tend to capture much more severe forms of impairment. Due to measurement inconsistencies, the first two waves of data are excluded from the analysis and the summated scale is available from Wave 3 to Wave 10.

The measure of cognitive impairment focuses on memory and executive function (Ofstedal, Fisher, & Herzog, 2005). Respondents were asked to complete a series of cognitive tasks (e.g., immediate and delayed word recall and backward counting from 20) and received a score of 0 for each correct answer and 1 for each incorrect one. A sum score ranging from 0 to 35 is created for Waves 3 to 9 where cognitive impairment is consistently measured. Prior studies have documented the construct (Zsembik & Peek, 2001) and predictive validity of this composite measure (Crimmins, Kim, Langa & Weir, 2011). We elect to remove HRS imputations in cognition, because by including an individual’s responses to other items and his/her demographic characteristics (e.g., age, race/ethnicity, and socioeconomic status) in the algorithm (Fisher, Hassan, Rodgers, & Weir, 2011), the imputation could artificially diminish intra-individual variability and introduce pseudo-associations between intra-individual variability and our focal independent variables (Little & Rubin, 1989).

Independent Variables

We identify each respondent’s age (in years; calculated from birth year) and gender (female = 1; else = 0). Race/ethnicity is measured by three dichotomized variables: White (=1, else=0; reference group), Black (=1, else = 0), and Hispanic (=1, else = 0). We measure socioeconomic status using years of education, individual earnings (ln-transformed), and non-housing assets (individual equivalent calculated from household assets; ln-transformed). Other covariates include married (=1, else = 0), working (=1, else = 0), obese (=1, else = 0), ever smoked (=1, else = 0), number of chronic conditions ever had (count; range [0–7]), and being couple respondents (=1, else = 0). Age, earnings, household assets, married, working, obese, comorbidity, and couple respondent are time-varying covariates measured at each wave for each individual. Gender, race, education, and ever smoked are time-invariant covariates.

Trajectory Model

We use multilevel mixed-effects models to estimate wave-based trajectories:

$$y_{ti}=\frac{\text{fixed-effects}}{{\beta }_0+{\beta }_1\text{Wave}+{\displaystyle \sum }_p{\beta }_p{X}_{pti}+{\displaystyle \sum }_q{\beta }_q{Z}_{qi}+}\frac{\text{random-effects}}{{\zeta }_{0i}+{\zeta }_{1i}\text{Wave}+{\epsilon }_{ti}.}$$

y _ti is the value of outcome y (i.e., functional limitations or cognitive impairment) for respondent i at time t, for i = 1:n and t = 1:T. β₀ is the intercept and β₁ is the slope of the trajectory indexed by wave. In preliminary analysis (not shown), we compared linear, quadratic, cubic, and quartic specifications of the trajectory and chose the linear form because the polynomial terms were nonsignificant and because polynomial specifications did not significantly improve model fit. X _pti represents time-varying covariates for p = 1:P, where P is the total number of such covariates and Z _qi represents time-invariant covariates, for q = 1:Q, where Q is total number of such covariates. Although functional limitations and cognitive impairment are measured in integers and exhibit skewed distributions, we assume an underlying normal distribution in the latent construct of functioning and therefore, recognize a censored normal distribution for this type of outcomes (Long, 1997). Accordingly, we use a Gaussian link for the trajectory model, which is appropriate for handling a censored normal outcome in mixed-effects trajectory models (Rabe-Hesketh & Skrondal, 2008).

This model partitions total variance into (a) between-individual (level-2, random intercept ζ _0i and random slope ζ_1i Wave) and (b) within-individual (level-1) residuals. The analytic focus of this article is the level-1 residual term, ε_ti. We estimate the variance of this term, which describes the typical deviation of a response from the estimated individual trajectory. For example, if the estimated variance of level-1 residual is 3, it means that a typical distance between a response and the individual mean is 1.73 ($\sqrt{3}\approx 1.73$). Level-1 residuals in adjusted trajectory models indicate intra-individual variability that remain unexplained even after accounting for predictors in the fixed-effects equation (Rabe-Hesketh & Skrondal, 2008).

Prediction Model of Intra-Individual Variability

We examine intra-individual variability in a multilevel growth curve modeling framework. Instead of using a time-constant within-person standard deviation score, we capture intra-individual variability by calculating mean absolute deviation scores at each measurement occasion. Doing so allows us to examine age-based patterns of intra-individual variability longitudinally. Compared with alternative approaches that rely on covariance structure analyses, our modeling framework has the advantage of accommodating unbalanced panel data structure and is more flexible on the inclusion and specification of predictors.

Specifically, from the trajectory models, we extract predicted level-1 residuals as the outcome. After log-transforming these values to correct for skewness, we estimate a random-effects Gaussian regression model with a maximum likelihood estimator, which is more appropriate for an unbalanced (i.e., incomplete) panel data structure (Rabe-Hesketh & Skrondal, 2008):

$$ln\left|{\epsilon }_{ti}\right|={\gamma }_0+{\displaystyle \sum }_k{\gamma }_k{W}_{kti}+{\displaystyle \sum }_l{\gamma }_l{S}_{li}+{\sigma }_u^2+{\sigma }_e^2.$$

$\left|{\epsilon }_{ti}\right|$ is deviation of a response from individual mean for individual i at time t, predicted by the intercept (γ₀) and time-varying (W _kti) and time-invariant (S _li) covariates. ${\sigma }_u^2$ and ${\sigma }_e^2$ account for between- and within-individual variances, respectively.

Panel Attrition

In panel studies of older adults, nonrandom attrition can mask the full degree of heterogeneity, by reducing inter- and intra-individual variability in the study outcome. This is especially problematic when studying late-life health, as older and sicker participants have a higher likelihood of death and loss to follow-up over the survey period. Differential survival is also associated with gender, race/ethnicity, and socioeconomic status (Rogers, 1992). In the analytic sample of functional limitations, about one fifth of the respondents died and one quarter dropped out during the panel. There is 10% mortal and 18% non-mortal attrition in the analytic sample of cognitive impairment. Preliminary analysis (not shown) suggests that panel attrition is greater among Black and Hispanic adults, men, and individuals with fewer years of education. Not accounting for these patterns may lead us to conclude that some groups have less intra-individual variability, solely because they have fewer observations due to premature mortality.

We use a two-stage Heckman selection bias model to correct parameter estimates (Heckman, 1979). Based on estimated patterns of death and nonresponse, we calculate two hazard-rate selection instruments (λ) for mortal and non-mortal attrition, respectively, and include them in the trajectory and prediction models as covariates (Stolzenberg & Relles, 1997). We recognize that this method is not without criticism (Bushway, Johnson & Slocum, 2007), yet it allows us to explicitly model selective survival across social categories, which can substantially affect the findings.

Analysis Plan

First, we estimate trajectory models of functional limitations and cognitive impairment with covariates and conduct residual diagnostics to examine whether there is intra-individual variability left unspecified. In the trajectory models, we allow for the assumption of homoscedasticity in level-1 residual variance, because our purpose in the first stage of the analysis is to establish the existence of patterns in the level-1 residuals. We show normal quantile plot of level-1 residuals and use the Shapiro-Wilk test to determine whether the level-1 residuals are roughly normally distributed. If the w statistic from Shapiro-Wilk test is significant (α = .001) and level-1 residuals exhibit a curve with large departure from the straight line in the normal quantile plot, it would indicate “structure” in residuals that were not accounted for in the trajectory models.

Second, we estimate the prediction models of intra-individual variability, where the predicted level-1 residuals obtained from the trajectory models for each individual at each available measurement occasion are regressed on age, gender, race/ethnicity, education, earnings, and assets, adjusting for baseline outcome as well as mortal and non-mortal attrition. If the age coefficient is significant and positive, it would mean that intra-individual variability in the selected outcome increases with age. If the coefficients associated with Blacks and Hispanics, for example, are significant and positive, it would indicate that these individuals have greater intra-individual variability than do Whites.

Results

As shown in Table 1, the average baseline score is 2.19 for functional limitations and 11.66 for cognitive impairment. Both outcomes increase over time. The average age of respondents at baseline interview is 61 years. More than half of the respondents are women. Of the respondents, 75% are White, 16% are Black, and 9% are Hispanic. The respondents on average have completed 12 years of education. Compared with the original HRS cohort, our sample has slightly smaller percentages of Blacks and Hispanics as well as men, which is likely a result of higher degree of panel attrition in racial/ethnic minorities and men prior to Wave 3. Because the differences are very small, our sample has the same degree of generalizability as the parent sample.

Table 1.

Means and Standard Deviations (in parentheses) of Study Variables

	Functional limitations	Cognitive impairment
	(n = 7,715)	(n = 6,985)
Wave 3	2.19 (3.00)	11.66 (4.49)
Wave 4	2.31 (3.09)	11.88 (4.73)
Wave 5	2.39 (3.10)	12.26 (4.56)
Wave 6	2.56 (3.08)	12.45 (4.54)
Wave 7	2.77 (3.18)	13.05 (4.44)
Wave 8	2.95 (3.24)	13.22 (4.67)
Wave 9	3.03 (3.26)	13.32 (4.62)
Wave 10	3.24 (3.22)	—
Age at baseline (in years)	60.54 (3.79)	60.68 (3.73)
Female	0.55	0.56
Black	0.16	0.16
Hispanic	0.09	0.09
Education (in years)	12.26(.29)	12.28 (3.11)
Earning(ln) at baseline	5.32 (5.00)	5.30 (4.99)
Assets(ln) at baseline	13.92(.27)	13.91(.27)
Married at baseline	0.74	0.74
Currently working at baseline	0.56	0.55
Ever smoked	0.62	0.61
Obese at baseline	0.26	0.26
No. of chronic conditions at baseline	1.28 (1.13)	1.26 (1.12)
Couple respondent	0.74	0.74
Died during panel	0.18	0.10
Ever attrited during panel	0.25	0.18
Average no. of responses during panel	6; Range [2–8]	4; Range [2–7]

Table 2 presents multilevel mixed-effects models predicting wave-based trajectories of functional limitations (Model 1) and cognitive impairment (Model 2). We first discuss the results for functional limitations. For every 2 years (one wave), functional limitations increase by 0.104 (SE = 0.018, p < .001). Women, Black adults, and individuals with lower levels of education, earnings, and assets tend to have greater functional limitations. Work status, obesity, smoking, and comorbidity are associated with functional limitations in expected directions.

Table 2.

Multilevel Mixed-effects Models Predicting Wave-based Trajectories of Functional Limitations and Cognitive Impairment Among White, Black, and Hispanic Adults Aged 55 and Older: HRS Cohort, Health and Retirement Study (1996–2010)^a

	Model 1		Model 2
	Functional limitations		Cognitive impairment
	(n = 7,715)		(n = 6,985)
	Coef.Sig.	(SE)	Coef.Sig.	(SE)
Fixed-effects
Intercept	6.037***	(0.607)	27.016***	(1.226)
Wave (= Wave -3)	0.104***	(0.018)	0.148***	(0.025)
Age (= Age -55)	−0.031***	(0.008)	0.062***	(0.012)
Female	1.049***	(0.054)	−1.061***	(0.078)
Black	0.240***	(0.073)	2.961***	(0.106)
Hispanic	0.108	(0.099)	1.107***	(0.142)
Education	−0.145***	(0.009)	−0.607***	(0.013)
Earnings(ln)	−0.012***	(0.003)	−0.007	(0.006)
Assets(ln)	−0.242***	(0.043)	−0.582***	(0.089)
Married	−1.171	(1.052)	−3.684	(1.931)
Working	−0.362***	(0.028)	−0.254***	(0.061)
Ever smoked	0.241***	(0.055)	−0.049	(0.078)
Obese	0.420***	(0.032)	−0.060	(0.256)
Morbidity	0.642***	(0.015)	0.227***	(0.025)
Couple respondent	1.035	(1.052)	3.472	(1.932)
Mortality (λ1)	1.281***	(0.070)	0.754***	(0.129)
Nonresponse (λ2)	−0.119	(0.061)	0.256**	(0.100)
Random-effects
Var (Intercept)	5.170***	(0.110)	7.896***	(0.243)
Var (Wave)	0.112***	(0.004)	0.101***	(0.009)
Cov (Intercept, Wave)	−0.260***	(0.016)	−0.241***	(0.038)
Var (Residual)	2.158***	(0.018)	7.124***	(0.080)
Model fit
Log likelihood	−91,457.02		−76,669.58
AIC	182,956.0		153,381.2
BIC	183,138.4		153,555.1

Notes. AIC = Akaike Information Criterion; BIC = Bayesian Information Criterion.

^aMaximum likelihood estimates. Gaussian distribution assumed.

**p < .01. ***p < .001.

Turning to cognitive impairment, for every 2 years, cognitive impairment increases by 0.148 (SE = 0.025, p < .001). Black and Hispanic adults tend to have greater cognitive impairment as compared with their White counterparts. Women have better cognitive functioning than do men. Education and assets are negatively associated with cognitive impairment, and comorbidity is positively associated with cognitive impairment. For both outcomes, our results are consistent with previous studies modeling trajectories of late-life functioning (e.g., Alley et al., 2007; Brown et al., 2012).

In the random-effects of the trajectory models, where we assess intra-individual variability, we find evidence in support of our hypotheses. The estimated variance of level-1 residuals is 2.158 (SE = 0.018, p < . 001) for functional limitations, suggesting that a typical distance between a response and the individual’s estimated average trajectory is 1.47 ($\sqrt{2.158}$). Individuals could gain or recover some difficulty in two functional tasks or a lot of difficulty in one task. Likewise, the estimated variance of level-1 residuals is 7.124 for cognitive impairment, suggesting a fluctuation of almost three incorrect items between waves ($\sqrt{7.124}=2.67$).

The next step of the analysis is to determine whether there are systematic patterns in these “error” terms. The w statistic of Shapiro-Wilk test is .942 (p < .001) for level-1 residuals in functional limitations and .995 (p < .001) for those in cognitive impairment, indicating violation of normality. Figure 2 presents normal quantile plots of level-1 residuals. For functional limitations, the level-1 residuals form an “S” shaped curve with considerable departure from a straight line. The heavy tails of the curve indicate excessive extreme values as compared with normally distributed residuals. A similar “S” shaped curve, albeit more muted than for functional limitations, is also found for cognitive impairment. Taken together, the findings reveal unexplained patterns of intra-individual variability in both outcomes.

Figure 2.

Normal quantile plot of level-1 residuals in adjusted health trajectories.

Thus, we undertake a multivariate analysis to determine whether there is systematic age and social patterning to the observed intra-individual variability. Table 3 presents results from random-effects Gaussian regression models predicting intra-individual variability in functional limitations and cognitive impairment. This model allows us to empirically test whether intra-individual variability in both outcomes varies by age, gender, race/ethnicity, and socioeconomic status and to examine the strengths of these associations. As hypothesized, we find an age-based increase in intra-individual variability for both outcomes. For each additional year of age, intra-individual variability in functional limitations increases by 1.019 (e^.019; b = 0.019, SE = .001, p < .001). Similarly, intra-individual variability in cognitive impairment increases by 1.004 (e^.004; b = 0.004, SE = 0.002, p < .05) for each additional year of age. In sum, results indicate that fluctuations in health status within individuals become greater as each individual ages.

Table 3.

Predictors of Intra-individual Variability in Trajectories of Functional Limitations and Cognitive Impairment Among White, Black, and Hispanic Adults Aged 55 and Older: HRS Cohort, Health & Retirement Study (1996–2010)^a

	Model 1		Model 2
	Functional limitations		Cognitive impairment
	(n = 7,715)		(n = 6,985)
	Coef.Sig	(SE)	Coef.Sig	(SE)
Fixed-effects
Baseline Functional Limitations	0.087***	(0.003)
Baseline Cognitive Impairment			0.004*	(0.002)
Age (= Age-55)	0.019***	(0.001)	0.006***	(0.001)
Female	0.126***	(0.001)	0.025	(0.015)
Black	0.064**	(0.024)	0.129***	(0.022)
Hispanic	0.081*	(0.032)	0.064*	(0.029)
Education	−0.024***	(0.003)	−0.049**	(0.013)
Earning	−0.014***	(0.001)	−0.001	(0.002)
Assets	−0.122***	(0.022)	−0.048*	(0.023)
Mortality (λ1)	0.197***	(0.024)	0.057**	(0.027)
Nonresponse (λ2)	−0.020	(0.020)	0.014	(0.021)
Intercept	0.849***	(0.311)	0.719**	(0.327)
Random-effects
Between-individual standard deviation	0.550***	(0.008)	0.268***	(0.012)
Within-individual standard deviation	1.086***	(0.004)	1.106***	(0.005)
Correlation	0.204***	(0.005)	0.056***	(0.005)
Model fit
Log likelihood	−68,963.621		−45,204.81
AIC	137,899.2		90,433.62
BIC	138,012.1		90,533.02

Notes. AIC = Akaike Information Criterion; BIC = Bayesian Information Criterion.

^aMaximum likelihood estimates. Gaussian distribution assumed.

*p < .05. **p < .01. ***p < .001.

Turning to the social patterning of intra-individual variability, results show systematic differences in intra-individual variability by gender, race/ethnicity, and socioeconomic status for both outcomes. We first discuss findings for functional limitations. Women have greater intra-individual variability than do men (b = 0.126, SE = 0.001, p < .001). Compared with White adults, Black adults have greater intra-individual variability (b = 0.064, SE = 0.024, p < .001). Hispanic adults also have higher intra-individual variability than do Whites (b = 0.081, SE = 0.032, p < .05). Post hoc analysis (not shown) suggests that Black and Hispanic adults are not significantly different with regards to intra-individual variability. There is a negative association between socioeconomic status and intra-individual variability in functional limitations. For each additional year of education, intra-individual variability lowers by 1.024 (e^.024; b = 0.024, SE = 0.003, p < .001). This suggests that the difference in intra-individual variability could be some difficulty in performing up to four functional tasks between individuals who completed high school and those who have college education. Higher earnings are associated with less intra-individual variability (b = −0.014, SE = 0.001, p < .001). Individuals with more assets are also more likely to have less intra-individual variability (b = −0.122, SE = 0.022, p < .001).

For cognitive impairment, we found no gender differences in intra-individual variability. Relative to White adults, Black adults have greater intra-individual variability in cognitive impairment (b = 0.129, SE = 0.022, p < .001). Hispanic adults have greater intra-individual variability relative to White adults as well (b = 0.064, SE = 0.029, p < .05), and post hoc analysis (not shown) suggests that they have less variability than do Black adults. Higher levels of education (b = −0.008, SE = 0.003, p < .01) and greater assets (b = −0.048, SE = 0.023, p < .05) are associated with less intra-individual variability. Individuals’ earnings, however, are not significantly associated with intra-individual variability in cognitive impairment. Collectively, the results consistently suggest that the more disadvantageous individuals tend to have greater intra-individual variability over time in health outcomes.

In addition, functional limitations at baseline are positively associated with intra-individual variability over time (b = 0.087, SE = 0.003, p < .001), indicating that individuals who are initially more functionally limited tend to be more variable over time. Individuals who have higher levels of cognitive impairment at baseline also show greater intra-individual variability over time (b = 0.004, SE = 0.002, p < .05). Respondents with a greater hazard of death during the panel tend to have greater intra-individual variability in functional limitations (b = 0.197, SE = 0.024, p < .001) and in cognitive impairment (b = 0.057, SE = 0.027, p < .01). Respondents with a greater hazard of nonresponse do not differ from their counterparts in intra-individual variability.

Discussion

Despite a long tradition of attending to issues of intra-individual variability in the gerontological literature (e.g., Baltes, 1979; Campbell & Buchner, 1997; Gill et al., 2006; Kim et al., 1996; Li et al., 2001; Martin & Hofer, 2004; Ram et al. 2011; Rowe & Kahn, 1997), we note with interest that systematic studies of its age and social patterning have not been fully integrated into studies of late-life health disparities. This may be partly due to the lack of sufficient data in the 1990s and earlier. With two-wave panel designs, the analytic focus lies necessarily in the direction and magnitude of change between two time points. Now, with the availability of many more observation points for each individual in panel surveys, refocusing sociological inquiry to include intra-individual variability in studies of late-life health can yield significant benefits for the field. The purpose of this study is to explore whether there is, indeed, systematic patterning, or a “signal,” to intra-individual variability or whether fluctuations in responses over time are “noise” that gets in the way of seeing the essential patterns of disparities.

Our first question was concerned with the potential age patterning of intra-individual variability in late-life health outcomes. We found that intra-individual variability increased systematically with age for functional limitations and cognitive impairment. Consistent with prior literature, our finding suggests that chronological age is a weak predictor of late-life disability (Gill et al., 2006) and cognitive decline (McArdle, Fisher, & Kadlec, 2007), which in turn challenges the view that there is a “normal” or “typical” pattern of age-related change during later life. Analyses that rely solely on averaged rates of change with age have diminished precision at upper ages, leaving variability in the lived experience of older adults unexplained. In this article, we present a straightforward method that can provide a more precise documentation of health dynamics across outcomes and study populations.

The magnitude of intra-individual variability that we found is of substantive concern. If intra-individual variability is small in a given indicator, it is possible that such “noise” is due to random errors. Our findings indicate, however, that at any particular time point, results from the average trajectory could potentially under- or over-estimate the outcome by 1 to 3 units. Substantively, this means that the average amount of variability for older adults can be difficulty in performing up to two functional tasks or answering up to three cognitive items incorrectly.

Interestingly, we found that intra-individual variability was greater for functional limitations than for cognitive impairment. This contrast in the degree of variability may indicate different underlying pathologies between selected health outcomes. Cognitive impairment tends to occur at more advanced ages, and its instability is more closely associated with acute health decline during end-of-life processes (Wilson, Beck, Bienias, & Bennett, 2007). Functional limitations, on the other hand, have a weaker relationship with age, because this measure is intended to capture difficulty in performing instrumental tasks in daily living as a consequence of chronic disease processes (Verbrugge & Jette, 1994). By design, this measure allows for more variation over time in gaining or recovering from limitations.

Our second question asks who is likely to have greater intra-individual variability in functional limitations and cognitive impairment? Based on our findings, women tend to have greater intra-individual variability in functional limitations, but there are no observed gender differences in intra-individual variability in cognitive impairment. Hispanic adults are not significantly different from White adults in average rates of change for functional limitations or cognitive impairment, yet they have significantly greater intra-individual variability than White adults for both outcomes. In addition to higher average differences in health trajectories, Black adults also show greater intra-individual variability relative to White adults on both outcomes. Individuals with lower levels of socioeconomic status have greater functional limitations and cognitive impairment on average and greater intra-individual variability over time as well.

These patterns are likely a direct consequence of social inequality. Men, White adults, and individuals with higher socioeconomic status remain in better and more stable health over time, as indicated by their lower limitations on average and less intra-individual variability over time. For the more disadvantaged, their worse average health is accompanied by greater fluctuations, suggesting that despite recoveries, the social environment that these individuals are embedded in continues to trigger, or fail to protect them from, repeated episodes of health deterioration. One possible explanation is that the health care received by those with limited resources may provide a temporary assistance, but because the care is of low quality, these individuals are still at higher risk for developing conditions, which in turn result in repeated onsets of limitations and impairment (Verbrugge, Reoma, & Gruber-Baldini, 1994). We note that, earnings and assets are time-varying covariates, measured at each wave for each individual, yet are very stable during the panel. Thus, their negative associations with intra-individual variability likely suggest a stabilizing function, whereby those with higher levels of earnings and wealth are less variable in health status over time.

We found distinct social patterns of intra-individual variability in both health outcomes, even though our adjustments for mortal and non-mortal panel attrition cannot possibly remove all nonrandom selectivity in the data. This means that the actual extent of intra-individual variability may be even greater and that its social patterning is more prominent, because the remaining selection effect that is not accounted for has likely reduced variability. The fact that greater intra-individual variability is observed among those at higher risk for mortality speaks to the robustness of this social patterning.

Taken together, the age and social patterning of intra-individual variability have implications for using panel data to study life course mechanisms, particularly cumulative dis/advantage processes. Cumulative dis/advantage theory places a heavy emphasis on inter-individual divergence—the tendency of systematic differentiation between cohort members—as the driver of age-based increase in cohort-level heterogeneity (Dannefer, 2003). In previous empirical studies of late-life health inequality, it has been left unchecked whether variability increases with age within individuals. If it is the case that increasing intra-individual variability with age, researchers may have overestimated the extent of inter-individual divergence in each cohort. Thus, the relative contribution of intra-individual variability to cohort-level heterogeneity needs to be examined before attributing heterogeneity exclusively to inter-individual divergence. This does not mean, however, that a pattern of increasing intra-individual variability with age would necessarily negate cumulative dis/advantage theory and lend support to an instability hypothesis. In contrast, the distinct social patterns of intra-individual variability raise the prominent possibility of heretofore unrecognized and undetected aspects to the way that accumulative mechanisms may operate over the life course.

Our examination of intra-individual variability over time in panel studies opens a new vista of research into the sociogenic influences of late-life health. In this study, we use a methodology that is most appropriate for the purpose of exploring patterns of intra-individual variability in incomplete panel data. With different research questions and data, several alternative approaches exist to push this line of inquiry even further. For example, if patterns of intra-individual variability in a given outcome have been identified, researchers can explicitly and more efficiently account for such level-1 heteroscedasticity by specifying a particular covariance structure (Rabe-Hesketh & Skrondal, 2008; also see Wallace & Green, 2013). When complete panel data are available or responses are missing completely at random, it is also possible to model repeated values of residuals as latent construct. Such an approach would be beneficial for testing alternative ways to capture and measure intra-individual variability.

We note three limitations in this study. First, the HRS is designed to interview respondents every 2 years. Measures taken at widely spaced time-scales may miss episodes of onset and recovery, potentially leading to mischaracterization of both intra-individual change and variability (Wolf & Gill, 2009). Also, a shorter time-scale makes measurement more sensitive to fluctuations (Newell, Mayer-Kress, & Liu, 2009). Future research should take into account how the time-scale used may obscure or reveal health dynamics.

Second, a “floor” effect embedded in the measures of the outcomes may have influenced the findings. The association we observe between baseline outcome and intra-individual variability may be induced by the floor effect. Moreover, because they are zero-censored, the measurement scales of functional limitations and cognitive impairment do not distinguish different levels of functioning when individuals have no limitations or impairment (Long, 1997). As a result, we may in fact underestimate variability for individuals with lower levels of limitations. Future research may observe an even greater degree of intra-individual variability, if using a scale that captures the full spectrum of physical and cognitive functioning.

Third, we elected to remove imputations in cognition by the HRS team, due to the concern that the imputations would artificially diminish variability and introduce pseudo-associations between independent variables and the outcome. Yet because item-missing in cognition measures are not missing at random, parameter estimates may be biased. Future research examining intra-individual variability should weigh carefully the trade-offs of excluding imputations in the outcome variable.

Despite the limitations, our study provides an example of how variations that were previously conceptualized as uninteresting “noise” can hold promises for sociological inquiry. The “signals” of late-life health inequalities that we identified cannot be reduced to random error or instability as a consequence of biological aging. The patterns suggest that the influence of social conditions on human aging can be explored in new empirical ways. It will be informative to use intra-individual variability in health as the study outcome to test extant conceptual models or to suggest new mechanisms through which life course health inequalities develop.

Funding

J. Lin was supported by an Advanced Study Fellowship via Department of Sociology at Case Western Reserve University and a National Institutes of Health Intramural Research Training Fellowship (Z01HG200335).