Application of Latent Variable Methods to the Study of Cognitive Decline When Tests Change over Time

Abstract

Background: The way a construct is measured can differ across cohort study visits, complicating longitudinal comparisons. We demonstrated the use of factor analysis to link differing cognitive test batteries over visits to common metrics representing general cognitive performance, memory, executive functioning, and language.

Methods: We used data from three visits (over 26 years) of the Atherosclerosis Risk in Communities Neurocognitive Study (N = 14,252). We allowed individual tests to contribute information differentially by race, an important factor to consider in cognitive aging. Using generalized estimating equations, we compared associations of diabetes with cognitive change using general and domain-specific factor scores versus averages of equally weighted standardized test scores.

Results: Factor scores provided stronger associations with diabetes at the expense of greater variability around estimates (e.g., for general cognitive performance, -0.064 standard deviation units/year, standard error = 0.015, vs. -0.041 standard deviation units/year, standard error = 0.014), which is consistent with the notion that factor scores more explicitly address error in measuring assessed traits than averages of standardized tests.

Conclusions: Factor analysis facilitates use of all available data when measures change over time, and further, it allows objective evaluation and correction for differential item functioning.

Figures

Figure 1. Graphical representation of cognitive tests available at each ARIC study visit

This figure is a structural equations model representing the final longitudinal model described in the Methods. Separate models were estimated for general cognitive performance, memory, executive functioning, and language; see Methods for details. WF: Word (phonemic) fluency (count of words recalled); BNT: Boston Naming Test (number of correct responses); AN: Animal (semantic) fluency (count of words recalled); DSB: Digit span backwards (sum of two trials of the maximum span); DSS: Digit symbol substitution (number of correct digit symbol pairs); TMT: Trail Making Test (seconds to complete); INCLRN: Incidental learning (number of correct digit symbol pairs recalled); LM: Logical memory (sum of recall for 2 stories); DWR: delayed word recall (sum of words recalled from one trial). Curved arrows between TMT-A, INCLRN, LMT, and DWR represent correlations between these items added due to analysis of normalized residuals (see Results).

Figure 2. Comparison of Two Approaches for Deriving Summary Scores from a Neuropsychological Test Battery

Measurement models for two approaches, averaging standardized versions of tests and single-factor analysis with categorical variables, are contrasted. Cognitive test scores are provided as examples; refer to Methods for the full neuropsychological test battery. DWR: delayed word recall; LMT: Logical Memory Test; TMT-A: Trail Making Test, Part A.

Figure 3. Item loadings and thresholds from the factor analyses for general cognitive performance

Graphical representation of results from the general cognitive performance factor analysis at the 2011–13 ARIC NCS visit. Factor loadings at right represent correlations between a test and the latent variable. Thresholds for responses to each test on the latent variable are shown by vertical boundaries in Appendix Figure 1, and denote the location along the latent variable of general cognitive performance (x axis) where tests provide optimal measurement precision. A histogram of the estimated general cognitive performance factor score in the 2011–13 participant sample, derived from the model that estimated these thresholds, is shown at the bottom. Some parameters (for TMT-A, DSS, BNT, WF, DSB) were estimated separately by race group to account for differential item functioning (see Table 2 and Methods). WF: Word (phonemic) fluency (count of words recalled); BNT: Boston Naming Test (number of correct responses); AN: Animal (semantic) fluency (count of words recalled); DSB: Digit span backwards (sum of two trials of the maximum span); DSS: Digit symbol substitution (number of correct digit symbol pairs); TMT: Trail Making Test (seconds to complete); INCLRN: Incidental learning (number of correct digit symbol pairs recalled); LM: Logical memory (sum of recall for 2 stories); DWR: delayed word recall (sum of words recalled from one trial).

Figure 4. Precision of General and Domain-Specific Cognitive Factors as a Function of Performance Level: Results from ARIC NCS (N=14,252)

Reliability for the general (top left), executive functioning (top right), language (bottom left), and memory (bottom right) factors are plotted over the range of their respective values. Plots for the first two visits overlap almost completely because the same tests were used. Horizontal dashed lines at reliabilities of 0.90 and 0.80 indicate acceptable reliability for within-persons analysis and between-persons analysis, respectively (33). Reliability = 1 – 1 / Information.