Constructing a Time-Invariant Measure of the Socio-economic Status of U.S. Census Tracts

Abstract

Contextual research on time and place requires a consistent measurement instrument for neighborhood conditions in order to make unbiased inferences about neighborhood change. We develop such a time-invariant measure of neighborhood socio-economic status (NSES) using exploratory and confirmatory factor analyses fit to census data at the tract level from the 1990 and 2000 U.S. Censuses and the 2008–2012 American Community Survey. A single factor model fit the data well at all three time periods, and factor loadings—but not indicator intercepts—could be constrained to equality over time without decrement to fit. After addressing remaining longitudinal measurement bias, we found that NSES increased from 1990 to 2000, and then—consistent with the timing of the “Great Recession”—declined in 2008–2012 to a level approaching that of 1990. Our approach for evaluating and adjusting for time-invariance is not only instructive for studies of NSES but also more generally for longitudinal studies in which the variable of interest is a latent construct.

A well-established literature documents that the socio-economic characteristics of the places in which we live influence our health and wellbeing.^1–7 For example, neighborhood socio-economic status (NSES), over and above individual socio-economic status,² can have lasting effects on outcomes ranging from hypertension,⁸ to allostatic load,⁹ disability,¹⁰ and depression.¹¹ Reviews of research on neighborhoods and health have suggested we need to better understand the role of critical periods, sequencing, and the accumulation of (dis)advantages over time.^6,12 Longitudinal studies hoping to address these questions, however, must first address the methodological challenge of appropriately measuring neighborhood characteristics over time: in particular, distinguishing between changes in the consequences of a neighborhood construct over time and changes in the measurement of the construct over time. The objective of this study is to address these challenges of incorporating time into the study of place by developing a measure of NSES and testing the stability of its measurement (time-invariance) from 1990 through about 2010. By so doing, we intend to not only produce a measure of the NSES of U.S. census tracts that can be used in longitudinal research and surveillance, but also elucidate whether and how indicators of NSES may have changed over the last several decades.

What Is NSES and How Has It Been Measured?

Research on neighborhood socio-economic conditions has its origins in Early Chicago School social theory.^1,6,13–15 Whether labeled “neighborhood disadvantage,” “neighborhood affluence and disadvantage,” or more broadly “neighborhood socio-economic status” (NSES), these studies have similarly employed factor analyses to describe the social and economic characteristics of U.S. census tracts, typically using decennial census data.^{8–10,16–26} Most commonly, a single factor is retained that is measured by all or a subset of the following indicators:¹ level of income, poverty, unemployment, public assistance, female-headed households, educational attainment, and employment in professional or managerial positions. However, these factor analyses have typically been carried out for a single measurement occasion. Thus, it is unknown and may not necessarily be the case that a single factor analytic solution for estimating NSES will be stable over time—i.e., that the factor structure, factor loadings, and item intercepts will be equivalent over time.

At least a decade of reviews highlight the need for longitudinal research on neighborhoods and individuals’ health and wellbeing.^6,7,12 However, nearly all known studies have employed static models of the neighborhood in which neighborhood conditions are measured at one point in time. In two known longitudinal studies with dynamic measures of NSES,^27,28 the assumption is made that a measure of neighborhood socio-economic conditions can be similarly estimated using three decades of decennial census data. This assumption of factorial invariance is a standard approach for dealing with potential changes in the measurement of a construct over time or age or across groups.²⁹ However, as in these two studies, the assumption of invariance is rarely tested. An unfortunate consequence is that comparisons over time may be biased and lead to false conclusions if invariance does not hold.³⁰

What Is Factorial Invariance and Why Does It Matter?

Factorial invariance refers to the equivalence of factor structures that are used to define latent variables. A latent variable is a “variable for which there is no sample realization”—that is, a variable that is not directly measured but instead is hypothesized as an explanation for relationships between measured variables.³¹ Invariance can be tested across groups (i.e., group-invariance),^32–35 or, as in this study, across time (i.e., time-invariance).^3,36–39 Invariance is tested in a sequence of increasingly restrictive models.⁴⁰ The first level of invariance is structural and evaluates whether the structure, or number of factors, are the same over time. If structural invariance fails to hold, the dimensionality of the latent variable has changed and comparisons will not be meaningful. However if structural invariance holds, weak invariance can be assessed by evaluating whether the factor loadings (or relationship between the indicators and the factor) are the same over time. If factor loadings change, then any potential changes in the level of the latent variable will not be reflected appropriately by changes in the measured variables. However, if weak invariance holds, then strong invariance can be tested by evaluating whether the intercepts (or the score) of an indicator variable is the same for the same level of the latent construct at each point in time.² Analogous to a regression model, the intercept of the indicator variables represent the expected score on the indicator when the latent variable is equal to zero. If the intercepts of the indicator variables remain constant (along with the factor loadings), as the mean score of the latent construct increases or decreases from a referent time point, then the measurement model meets strong invariance. However, as above, if strong invariance fails to hold and the assumption is made that the measure is time-invariant, then estimates of the latent construct will be biased and not comparable over time. Uncorrected, the resulting implication of a researcher applying a measure that fails the test of strong invariance is that a change in the level of construct will be interpreted from what is in actuality a change in the scaling of one (or more) of the indicators of the construct.

Assessment of these potential forms of measurement instability and adjustment for any form of time-invariance is critical in producing a measure of NSES—or any other latent measure—for unbiased assessment of longitudinal research questions. In addition, the process of evaluating and constructing a time-invariant measure allows us, and other researchers, to develop new insights about potential stability and change in the indicators and measurement of the construct over time.

Methods

Data

U.S. Census Bureau data on the social and economic characteristics of U.S. census tracts are obtained from the 1990 and 2000 decennial census long-forms^41,42 and the 2008–2012 American Community Survey (ACS).⁴³ The ACS, like the decennial census long-form it has replaced, is a national survey of all U.S. housing units and group living quarters. Due to the smaller but more frequent sampling conducted by the ACS, however, data for geographic areas as small as census tracts are released in 5-year estimates, beginning with 2005–2009. We select the 2008–2012 ACS because the centroid is ten years after the 2000 census. Census tracts were employed as the proxy for neighborhood with the study sample restricted to those observed at all three assessments in 1990, 2000, and 2008–2012 (N = 65,174). U.S Census Bureau data for the 1990 Census, 2000 Census, and 2008–2012 ACS use, respectively, the 1990, 2000, and 2010 census tract boundary definitions. These data were harmonized to the 2000 census tract boundaries using a transformation matrix we calculated from the Longitudinal Tract Data Base (LTDB⁴⁴).³

Measures

Nine indicators of NSES were considered:

• Median household income;

• Proportion of households with income below the federal poverty level;

• Level of education;

• Proportion of the population age 16 years or older that is unemployed;

• Proportion of civilian workers age 16 years or older in management, professional, and related occupations;

• Proportion of households that receive public assistance income;

• Proportion of female-headed households (i.e., no husband present) with children under age 18 years;

• Proportion of households with crowded housing (i.e., more than one occupant per room); and

• Median value of owner-occupied housing units.

Median household income and median housing value are reported in dollar values that we adjusted for inflation using a 2000 referent.⁴⁶ The measure of the level of education is calculated from the proportion of the population age 25 years and older that reports educational attainment: (a) less than a high school diploma or general education development (GED) equivalent; (b) a high school diploma or GED equivalent, but not a bachelor’s degree; and (c) a bachelor’s degree or higher.⁴ The reference periods for the reporting of household income and any income from public assistance,⁵ as well as employment status,⁶ differ between the decennial censuses and the ACS.^47,48 The Census Bureau suggests that these variables (and variables, such as poverty status, derived from them) can be compared between the decennial censuses and ACS, albeit with caution.⁴⁹ In addition, the proportion of the census tract employed in management, professional and related occupations is obtained from the estimates for detailed occupational categories reported in the decennial censuses and ACS. These detailed occupational categories are based on the U.S. Bureau of Labor Statistics six-digit Standard Occupation Code (SOC) system for 1990, 2000, and 2010. Although reporting categories changed between 1990 and 2000 and again in 2010 on the basis of changes in the SOC, these changes largely entailed those in subcategories below the top level of SOC reporting categories denoting management, professional, and related occupations.^50,51

Data Preparation and Statistical Analysis

We first examined the distributions of the variables and carried out transformations so that skewed variables more closely approximated a normal distribution. After examining variable distributions, a natural logarithm transformation was applied (adding a constant, where necessary). In addition, because the estimation algorithms used in the confirmatory factor analysis models (described below) may not converge when variances differ across indicator variables by more than an order of magnitude, we multiplied indicators by a constant to ensure that variances were broadly similar.

Estimation of a latent construct describing NSES was carried out using exploratory and confirmatory factor analysis with Mplus version 7.11.⁵² Models were estimated using the maximum likelihood (robust) algorithm which provides estimates of model fit that are equivalent to maximum likelihood, with corrections to standard errors and model fit to account for non-normality in the data.^53–55

The data analysis procedure for testing time-invariance typically starts with a measure or measurement instrument that has a known dimensionality. Because the dimensionality of NSES is unknown, our first analysis combines the testing of dimensionality and configural invariance. Based on our review of the previous NSES literature, we fitted a confirmatory factor analysis (CFA) model with a single factor at each time using the nine indicators described above. Unique variances of the equivalent variables were correlated across time. However, the fit of this CFA model (model A1) was poor. Given that our initially specified model had failed we therefore proceeded with exploratory factor analysis to develop an initial model, using maximum likelihood extraction and geomin rotation.⁵⁶ Using this exploratory factor analysis approach, we identified five NSES indicator variables which appeared to fit a single factor structure at each assessment. We then tested for time-invariance of the NSES measurement instrument defined using these indicators within a confirmatory factor analysis framework. A confirmatory factor analysis approach for modeling NSES longitudinally involves estimating all of the following at each time point: (a) a matrix of factor loadings for the relationship between each indicator variable and the latent construct; (b) a vector of intercepts for each indicator variable; (c) a vector of means of the latent variables, (d) a matrix of variances and covariances of the latent variables; and (e) a matrix of residual variances and covariances for the indicator variables.

Several parameter constraints are required to statistically identify the longitudinal model for NSES. To identify the mean and variance of the latent variable at one point in time, it is necessary to identify a reference variable and constrain the loading and intercept of this parameter at each time point. The reference variable can be thought of as ‘anchoring’ the latent variable and is typically chosen to be the indicator variable believed to be most closely related to the latent construct.³¹ We selected median household income as the reference variable and constrained the loadings of this variable to 1.00. Similarly, in order to statistically identify potential change in the latent construct, it was necessary to anchor the mean of the latent variable in time. We selected the first time point (1990) as the referent time point for the latent variable and constrained the mean of the latent variable to be zero at this point. Again, any value could have been employed, but zero was most convenient for model interpretation because it allowed us to observe change in the mean of the hypothesized latent variable (NSES) over time, relative to the first time point once a time-invariant model of NSES was identified. To identify the mean of the latent variables at the later time points, we constrain the intercept of the reference variable to be equal at each time point. By selecting the above parameter constraints to achieve statistical identification we also ensured that the coefficients for the intercepts of the indicator variables could be readily interpreted and evaluated for time-invariance. The intercept of the indicators are interpreted, as in regression, as the expected value of the variable when the mean of the latent variable (which functions as a predictor here) is equal to zero. If the latent variable changes over time, and all of the indicator variables change in a consistent fashion, then the intercepts of the indicator variables will be constant over time.

We employed conventional statistical methods to test for configural, weak, and strong time invariance.^40,57 Weak invariance was tested by comparing a model in which the set of factor loadings for each respective indicator were constrained to equality over time (model B3) versus an otherwise equivalent model (model B2). Strong invariance was tested by comparing a model in which the set of intercept coefficients for each respective indicator were additionally constrained to equality over time (model B4) versus the unconstrained model (model B3).

Given the large sample size, we expected chi-square tests to be overpowered and lead us to reject models based on small discrepancies. Therefore, the RMSEA (root mean square error of approximation⁵⁸) and CFI (comparative fit index⁵⁹) were better choices for evaluating global model fit. We employed a threshold value of 0.06 to indicate adequate fit for RMSEA and 0.95 for CFI;⁶⁰ we also evaluated aspects of local model fit (e.g., residuals, modification indices and standardized expected parameter changes). In addition, we use a ΔCFI of greater than 0.010 to indicate a meaningful reduction in model fit when constraints were added.⁶¹ We use modification indices in conjunction with standardized expected parameter changes to guide model modification.⁶²

Results

Table 1 shows means and standard deviations for each of the indicator variables prior to and post transformation in 1990, 2000, and 2008–2010.

TABLE 1.

Descriptive statistics for variables describing neighborhood socioeconomic characteristics of U.S. census tracts by assessment year(s), pre- and post-transformation (N=65,174)

Variable and year(s)	Pre-transformation		Transformation of variable (Y)	Post- transformation
	Mean	SD		Mean	SD
Household income (median in dollarsa)
1990	39,048.46	18,122.98	ln(10 + Y)	10.47	0.46
2000	44,249.33	20,760.14		10.60	0.45
2008–2012	40,128.05	19,805.98		10.49	0.47
Poverty (proportion)
1990	0.13	0.12	ln(0.1 + Y)	−1.55	0.43
2000	0.13	0.11		−1.57	0.41
2008–2012	0.15	0.12		−1.46	0.42
Educational level
1990	0.94	0.28	Y × 10	9.39	2.80
2000	1.02	0.29		10.24	2.86
2008–2012	1.11	0.27		11.15	2.73
Unemployment (proportion)
1990	0.07	0.05	ln(0.01 + Y)	−2.70	0.56
2000	0.06	0.06		−2.79	0.61
2008–2012	0.10	0.06		−2.34	0.53
Professional/ managerial occupations (proportion)
1990	0.25	0.12	Y × 10	2.50	1.22
2000	0.32	0.14		3.18	1.40
2008–2012	0.37	0.16		3.74	1.60
Public assistance (proportion)
1990	0.08	0.08	ln(Y × 10 + 0.1)	−0.91	0.83
2000	0.04	0.05		−0.49	0.47
2008–2012	0.03	0.04		−0.41	0.35
Female-headed households (proportion)
1990	0.11	0.10	ln(0.01 + Y)	−2.30	0.64
2000	0.11	0.09		−2.34	0.70
2008–2012	0.12	0.10		−2.28	0.77
Crowded housing (proportion)
1990	0.05	0.07	ln(Y × 10 + 0.1)	−0.60	0.77
2000	0.06	0.09		−0.71	0.90
2008–2012	0.04	0.06		−0.45	0.55
Housing unit value (median in dollarsa)
1990	124,881.55	103,603.53	ln(0.01 + Y)	11.22	2.21
2000	134,904.00	110,838.00		11.34	2.20
2008–2012	124,731.27	100,068.51		11.38	1.48

Note: SD standard deviation

^aReported dollar values are adjusted for inflation using the CPI-U-RS with a 2000 referent

The process of evaluating the time-invariance involved a series of models whose goodness of fit statistics are detailed in Table 2. The first step was to assess configural invariance and dimensionality of NSES over the three assessments. A single factor model (model A1) failed to adequately account for the data (RMSEA = 0.062 and CFI = 0.875). We therefore conducted EFA and identified a unidimensional subset of the variables: median household income, educational level, proportion unemployed, proportion below the poverty level, and proportion of female-headed households.

TABLE 2.

Fit statistics for confirmatory factor analysis models of neighborhood socio-economic status, testing levels of time-invariance

Model	Chi-square (df)	RMSEA	CFI	ΔCFI
A1: Configural invariance, 9 indicator variablesa	73,527 (294)	0.062	0.875	NA
B1: Configural invariance, 5 indicator variablesb	17,118 (72)	0.060	0.966	NA
B2: Model B1 with correlated errorc	15,122 (69)	0.058	0.970	+0.004
B3: Model B2 with weak invarianced	20,068 (77)	0.063	0.960	−0.010
B4: Model B3 with strong invariancee	86,023 (85)	0.125	0.829	−0.131
C1: Model B4 with intercepts correctedf	21,090 (85)	0.063	0.958	NA

Notes: df degrees of freedom, RMSEA root mean square error of approximation, CFI comparative fit index, ΔCFI change in comparative fit index, CFA confirmatory factor analysis

^aModel A1 is a CFA model estimated using 9 indicator variables for the socio-economic status of U.S. census tracts (i.e., household income, educational level, housing unit value, and proportions of poverty, unemployment, professional/managerial occupations, public assistance, female-headed households, and crowded housing)

^bModel B1 is a CFA model estimated using five indicator variables (i.e., household income, educational level, and proportions of poverty, unemployment, and female-headed households)

^cModel B2 adds to model B1 a correlation of the residual error terms for poverty and household income

^dModel B3 adds to model B2 the constraint that factor loadings for respective indicators are equal over time

^eModel B4 adds to model B3 the constraint that the intercepts for respective indicators are equal over time

^fModel C1 estimates model B4 using data on the five indicator variables that corrects for strong invariance

Having identified a unidimensional set of items that appeared to measure the same construct over time, we next proceeded to formally test the time-invariance of these items. We refer to this sequence of CFA models as model series B (See Table 2). The first model in the series (model B1) tested the configural invariance of a single factor model measured with the five indicator variables. It fit the data adequately (RMSEA = 0.062 and CFI = 0.966). Examination of the modification indices and standardized parameter estimates suggested that a model that incorporated a correlation in the residual variance of the variables median household income and proportion below the poverty level would fit better, and indeed the fit statistics improved considerably for model B2 with this added parameter.

Our next step was to test for weak factorial invariance by constraining factor loadings to equality across all three assessments (model B3). Although the fit worsened when this constraint was added, the decrement to CFI was negligible (∆CFI = −0.010, Table 2), and thus allowed us to retain the hypothesis of longitudinal invariance of the factor loadings. As further (qualitative) evidence of weak time invariance, consider the stability over time of the factor loadings for model B2 in which these parameters were allowed to be freely estimated and their close equivalence to the constrained factor loadings for model B3 (Table 3). Recall also that because median household income was selected as the reference variable, the factor loadings for this indicator are constrained to 1.00.

TABLE 3.

Factor loadings from longitudinal confirmatory factor analysis models of neighborhood socioeconomic status in which factor loadings are unconstrained (model B2) versus constrained (model B3 and model C1)

Variable	Factor loadings unconstrained			Factor loadings constrained
	Model B2a			Model B3b	Model C1c
	1990	2000	2008–2012	All time points	All time points
Median household income	1.00	1.00	1.00	1.00	1.00
Educational level	4.85	5.13	4.44	4.88	4.88
Unemployment	−1.01	−1.09	−0.72	−0.96	−0.96
Female-headed households	−1.11	−0.96	−1.01	−1.09	−1.09
Poverty	−0.96	−0.93	−0.88	−0.93	−0.93
Standardized loadingsd
Median household income	0.92	0.92	0.93	0.92	0.92
Educational level	0.74	0.74	0.72	0.74	0.74
Unemployment	0.77	0.74	0.60	0.75	0.75
Female-headed households	0.74	0.65	0.59	0.73	0.73
Poverty	0.94	0.93	0.92	0.93	0.93

All factor loadings are highly statistically significant (p < 0.0001)

^aModel B2 is estimated using five indicator variables for the socio-economic status of U.S. census tracts, with correlated errors of two of the indicator variables. Median household income is selected as the reference variable for statistical identification of all models, and thus the factor loadings are constrained to 1.00 at each time point

^bModel B3 adds to model B2 constraints on the factor loadings, but like model B2 allows the indicator intercepts to be freely estimated

^cModel C1 adds to model B3 constraints on intercepts for each respective indicator to be equal over time, and it adjusts the data for strong invariance over time. All factor loadings are highly statistically significant (p < 0.0001)

^dModel C1, the standardized loadings will change slightly over time due to differences in the variance of the indicator variables at each time point. Thus, we display the standardized loadings for the 1990 assessment

The final step was to consider the stability of the indicator intercepts over time (model B4), or strong factorial invariance. To test strong invariance, we constrained the intercepts of all equivalent variables to be equal across the three assessments. In implementation, this means that the constrained intercepts will be equal to a weighted average of the unconstrained intercepts (see Table 4). As reported in Table 2, model B4 had considerably worse fit than model B3 (∆CFI = −0.131) which indicated that we cannot conclude that the measure is strongly invariant over time. As further (qualitative) evidence of the lack of time-invariance of the indicator intercepts, consider how the freely estimated values of the intercepts for model B3 reported in Table 4 change over time. Recall that in order to statistically identify the time trend in NSES in all of the longitudinal models, we employ 1990 as the referent time point and median household income as the referent indicator variable. Thus, in model B3 the indicator intercepts in 1990 are equal to the means of the respective variables at 1990 in Table 1, and the intercept for median household income is constrained to be equal at all time points. Inspection of the values of the indicator intercepts in model B3 show that the indicators with the largest changes are educational level and unemployment. For both indicators, the intercepts are increasing and thus indicate that the rate of change in education and unemployment is out of pace with the rate of change in the other indicators. In order to achieve the objective of employing a consistent measurement instrument for NSES at each time point, this change in the scaling of the indicator variables relative to one another will need to be addressed.

TABLE 4.

Indicator variable intercepts from longitudinal confirmatory factor analysis models of neighborhood socio-economic status in which indicator variable intercepts are unconstrained (model B3) versus constrained (models B4 and C1)

Variable	Indicator intercepts unconstrained			Indicator intercepts constrained
	Model B3a			Model B4b	Model C1c
	1990	2000	2008–2012	All time points	All time points
Median household income	10.47	10.47	10.47	10.47	10.47
Educational level	9.39	9.61	11.06	10.35	9.39
Unemployment	−2.70	−2.67	−2.32	−2.59	−2.70
Female-headed households	−2.30	−2.20	−2.26	−2.28	−2.30
Poverty	−1.55	−1.45	−1.44	−1.50	−1.55

All indicator intercepts are highly statistically significant (p < 0.0001)

^aModel B3 is estimated using five indicator variables for the socio-economic status of U.S. census tracts, with correlated errors of two of the indicator variables and constraints on the factor loadings (not shown) for each respective indicator to be equal over time. Median household income is selected as the reference variable and 1990 is selected as the reference time point for statistical identification of all models; thus the indicator intercepts for median household income are constrained to their 1990 value at each time point

^bModel B4 adds to model B3 constraints on the intercepts for each respective indicator to be equal over time

^cModel C1 is equivalent to model B4, and also adjusts the model for strong invariance over time

In summary, our CFA analyses provided evidence supporting two out of the three levels of longitudinal invariance: i.e., configural invariance and weak factorial invariance, but not strong factorial invariance. The poor fit of the model testing strong factorial invariance implied that, for the same overall level of NSES, the expected value of the measured variables was not equal. Bias that arises from a lack of strong invariance can be corrected by adding a constant to measured variables to correct for change; in the item response theory literature, this lack of strong invariance is referred to as differential item functioning.⁶³ The constant that is added is the difference between the intercepts shown in Table 3. For example, for education in 2000, one would add the constant (9.39 − 9.61=) −0.22 to the values of education in the 2000 wave. When we corrected the data on our indicator variables for strong invariance, and then tested the fit of a model in which we constrained both the factor loadings and indicator intercepts to be equal (model C1), we observed about as good of fit (RMSEA = 0.063 and CFI = 0.958) as the reference model, model B2, in which the loadings and intercepts were unconstrained and allowed to vary freely. Our final, best time-invariant model of NSES was thus model C1.

In Table 4, we compare the factor loadings from the unconstrained reference model (model B2) and our final time-invariant model (model C1). As expected, on the basis of the presence of factorial invariance in model B2, all loadings are similar in magnitude over the three assessments and about equal to those of model C1. The bottom panel of Table 4 displays the standardized loadings which are useful for comparing the magnitude of loadings across indicator variables. Although all variables are good indicators of NSES with loadings above 0.60, the strongest indicators are median household income and proportion below the poverty level, both of which have standardized loadings greater than 0.90 in model C1 and at each assessment in model B2.

In Table 5 we summarize the characteristics of the final latent NSES measure (using model C1), including the mean score of NSES indexed to 1990 (i.e., with a mean of zero in 1990), its variance and composite reliability. We find that NSES increased from 1990 to 2000 by $\left(\frac{0.13-0.00}{\sqrt{0.41}}=\right)0.20$ standard deviation units, but then decreased by nearly the same amount, (i.e., $\frac{\left(0.02-0.13\right)}{\sqrt{0.40}}=-0.17$ standard deviation units) by the 2008–2012 assessment. The composite reliability of the latent variables is high, with values above 0.95 at each assessment. The correlation of NSES over assessments is also very high with the correlation of 0.97 between 1990 and 2000 assessments and 0.92 between 2000 and 2008–2012 assessments, indicating stability of the NSES measure over time.

TABLE 5.

Characteristics of the latent measure for neighborhood socio-economic status (NSES) estimated in the final confirmatory factor analysis model (model C1)

	Assessment
	1990	2000	2008–2012
Mean of NSESa	0.00	0.13	0.02
Standard deviation of NSES	0.41	0.40	0.40
Composite reliability of NSES	.953	.951	.951
Correlation of NSES over assessments
Assessment 1990	1.00
Assessment 2000	0.97	1.00
Assessment 2008–2012	0.92	0.97	1.00

Model C1 is estimated using five indicator variables for the socio-economic status of U.S. census tracts that are corrected for strong invariance over time, with correlated errors of two of the indicator variables and with constraints on the factor loadings and intercepts for each respective indicator to be equal over time

^aThe mean of the latent measure for NSES is constrained to zero in 1990 for identification purposes

Discussion

Our objective was to develop a time-invariant measure of NSES for 1990 through about 2010. We achieved this goal using five indicators and a unidimensional model that met conditions for configural and weak factorial time-invariance (pertaining to factor structure and factor loadings) but not strong factorial time-invariance (pertaining to indicator intercepts). Change in indicator intercepts is also described as differential item functioning and can lead to bias in the longitudinal application of a measure.⁶⁴ In our final model, we corrected for differential item functioning and found that, although NSES increased between 1990 and 2000 (by about 0.2 standard deviations units), this gain was almost entirely lost about 10 years later. The pattern of expansion and collapse we observe for NSES parallels changes in housing, financial and labor markets over these decades, whereby the Great Recession reversed the “economic boom” of the 1990s. Other studies have described the negative consequences of the Great Recession for levels of employment, income and poverty,⁶⁵ as well as family arrangements and their potential for leveraging resources.^66,67 To our knowledge, ours is the first to describe the apparent consequences for trends in socio-economic conditions of U.S. census tracts.

Through the process of developing our final time-invariant NSES measure, we determined that four of the hypothesized indicators failed to consistently load with the other indicators at all three assessments. We speculate that macro social and economic changes occurring over the 1990s and 2000s may account for the changing relationship between these indicators and NSES. For example, fundamental restructuring of policies to assist low-income families initiated with the 1996 Welfare Reform, including conditions on assistance such as time-limits,⁶⁸ may have made the proportion of individuals receiving assistance at any given time in a community a poorer indicator of that community’s underlying NSES. Similarly, the poor performance of the proportion employed in managerial and professional occupations may reflect the recent critique of “big class” stratification models,^69–71 including that they have become insufficiently nuanced to capture current class cleavages.⁷ Finally, we suspect that the housing market bubble, collapse, and subprime mortgage crisis⁷³ may have changed the relationship between socioeconomic position and our housing-related variables making these indicators too volatile or inadequately discriminating of NSES.

With respect to the time-invariance of the indicator intercepts, we observed that educational composition changed the most with a higher level of education required to attain the same level of NSES in each decade. These results are consistent with findings from our descriptive statistics and elsewhere,^74,75 that the upward trend in U.S. educational attainment was not equally matched by changes in other socioeconomic indicators. Our adjustments for strong time-invariance ensures that, in the application of the NSES model, these changes in the measurement of NSES will not be misinterpreted as changes in the consequences of NSES.

While there are many possible alternative indicators and models of NSES, and though we drew upon existing literature to inform our selection, our indicators were necessarily restricted to those from publicly accessible data on census tracts. The limitations of this approach while still the most feasible for nationally-generalizable longitudinal research, are well established.^2,6,7 Furthermore, as we describe in our methods, a reference variable is required in CFA for purposes of identification. Standard practice is to select the variable hypothesized to be most closely related to the latent variable, and although both poverty and income met this criterion,⁷⁶ income offered a more intuitive interpretation. It is important to note that our findings on the lack of intercept stability over time are predicated on our choice of income as the reference variable. Finally, it was not possible to assess time-invariance for intercensal years when no publicly available nationally inclusive census tract data exists, and it was beyond the scope of this paper to assess time-invariance using censuses prior to 1990 or earlier ACS 5-year estimates (beginning in 2005–2009). Thus, our findings should not be extrapolated to points prior to 1990 and should be applied cautiously to intercensal years. That said, we have conducted sensitivity analyses using the 2005–2009 ACS and found similar results on the five-factor unidimensional structure, presence of configural and weak time-invariance, and absence of strong time-invariance. We have also tried to be careful about language throughout the text to recognize that, although the centroid of the ACS 2008–2012 assessment is 2010 about 10 years after the 2000 Census, multiyear estimates capture a “window” of time rather than time-point.^77,78

All latent variable models suffer from the disadvantage that they cannot be objectively defined—this is the indeterminacy problem.^31,79 Hence, there are potentially other models of NSES which may also evidence the properties of fitting the data well and meeting statistical qualifications for time-invariant measurement. As with any latent construct, we therefore caution the reader against over-interpretation and/or reification of the construct⁸⁰ The latent variable is a hypothesized variable which explains the relations among the variables. It cannot attain the status of ‘truth’ but may be strengthened through additional independent validation studies. We nonetheless subscribe to the view that an invariant latent variable based approach is useful for two reasons. First, the use of a latent variable rather than a (potentially large) number of separate indicator variables leads to more parsimonious statistical models. Second, latent variable models are in use by NSES researchers, regardless. Yet, on the basis of our findings, it is likely that these models are not time-invariant and thereby are introducing bias into longitudinal inferences about NSES change or the consequences of NSES change. By ensuring that our NSES measure is consistent over time, we introduce additional rigor into the research on time-varying assessment of latent contextual measures. Finally, there is no reason to believe that our measurement approach, or any other, will continue to function coherently into the future (or further into the past). The utility of different indicators may change—for example, if an overarching majority of individuals obtain a college degree in the future, education will cease to be a useful indicator of NSES. It is possible that models developed using methods for accelerated longitudinal designs⁸¹ or integrative data analysis⁸² might be useful in such a case. In these designs, indicator variables can be added or removed over time as they become appropriate, or cease to be appropriate, retaining the comparability of the latent variable. The disadvantage of such an approach is that they would require a stronger theoretical understanding of the nature of the NSES construct than we believe currently exists and a much longer series of measurement occasions then was feasible within the scope of the existing study.

Our final NSES measure provides, to our knowledge, the only such measure to have been evaluated for, and adjusted to ensure, time-invariance. We, thus, offer not only a research tool for the longitudinal study and surveillance of NSES, but a more general methodology for measuring changing neighborhood conditions. It is unclear how much the failure to address potential time-invariance may bias inferences about the accumulation and change in neighborhood conditions, but continuing debate about neighborhood change as a lever for social policy underscores the importance of examining these questions using the methodologies and tools from this study.