8/20/2018

Learning Objectives

  • Formative versus reflective factors
  • Capturing residual from regression analysis as latent variable
  • Decomposing cognitive variable into orthogonal components
    • Demographic
    • Brain
    • Residual not explained by demographic and brain variables
  • Tips for navigating modeling complexities

Problem and Dataset

  • Goal is to replicate modeling approach in:
    • Reed et al. Measuring cognitive reserve based on the decomposition of episodic memory variance. Brain. 2010;133(Pt 8):2196-2209.
  • Data comes from UC Davis Alzheimer's Disease Center
  • Real data, deidentified
  • Mplus input, data, and output files are included in Reserve_Tutorial.zip
  • Models should run in Mplus

Variables in Model

  • Memory - cross-sectional episodic memory score
  • BM - total brain volume
  • HC - total hippocampal volume
  • WMH - white matter hyperintensity volume
  • ICV - intracranial volume
  • Education - years of education (centered at 12)
  • Male - gender, 1 if male, 0 if female
  • AA - race/ethnicity, 1 if African American, 0 if Caucasian or Hispanic
  • Hispanic - race/ethnicity, 1 if Hispanic, 0 if Caucasian or African American

Residual Reserve Index Model

Formative and Reflective Factors

  • Reflective factors - the latent factor is considered to cause the observed indicators
    • arrows go from factor to indicators
    • more common usage
  • Formative factors - the latent factor is caused by the observed indicators
    • is a weighted linear combination of the observed indicators

Residual Reserve Index Model

Highlights of Residual Reserve Index Model

  • Memory is decomposed into orthogonal (uncorrelated) components
    • Variance component due to demographic variables (MemD)
    • Variance component due to brain variables (MemB)
    • Variance not related to demographics or brain (MemR)
    • Error variance (assuming reliability of 0.85, error variance component fixed at 0.15 * total Memory variance)
    • Squares of MemD, MemB, and MemR loadings (*'s on paths to Memory) show percent of Memory variance explained by each component

Highlights of Residual Reserve Index Model (continued)

  • MemD and MemB are formative factors
    • represent linear combinations of demographic and brain variables that optimally explain Memory
  • Observed brain variables are assumed to have reliability of 0.90
    • 10% of their total variance is fixed as error variance
  • BM and HC are residualized/adjusted for ICV within the model

Highlights of Residual Reserve Index Model (continued)

  • Use of MemD and MemB formative factors makes it possible to decompose Memory into three discrete variance components
    • This was of substantive interest in original publication but was not required to estimate residual reserve index
  • MemR could be estimated without using MemD and MemB
    • Simple residual of Memory independent of the demographic and brain variables

Model Development

Model 1 - mem_res_1a

  • Shows basic specification of model
  • MODEL CONSTRAINT feature is used to set variances for dichotomous variables
    • variance of binomial variable is p(1 - p)
  • Note warning in output about estimating parameter 54, ICV variance
    • This value will be fixed at sample variance in subsequent models

Model 2 - mem_res_2a

  • ICV fixed at sample variance
  • Note in Tech4 Output that estimated variance of MemD is 27.495 and MemB is 6.955
    • These values are arbitrary and are set by the scale of measurement
    • Different scales having variances of 1.0 might be more convenient

Model 3 - mem_res_3a

  • Fixed regression coefficients for educ_12 (MemD) and gml (MemB) are changed to rescale factor variances
    • values chosen are 1/sqrt(variances from Tech4, model 2)
    • variances in Tech4 are now ~1.0
    • model fit is identical to model 2

Model 4 - mem_res_4a

  • An external outcome (exec - executive function) is regressed on MemD, MemB, and MemR
  • Overall model fit is poorer because model does not capture all pathways from demographic and brain variabes to exec

Model 5 - mem_res_5a

  • MemR is regressed on external variables corresponding to clinical diagnosis
    • dem - 1 if Dementia, 0 if Normal or MCI
    • mci - 1 if MCI, 0 if Normal or Dementia

Model 6 - mem_res_6a

  • We also regress MemD and MemB on dem and mci
    • Model does not converge
    • dem and mci become formative indicators for MemD and MemD
      • since they are common indicators for orthogonal factors (MemR also), model as specified cannot be estimated
      • This is not a problem when MemR alone is the dependent variable
  • This shows the complexity of using this type of model to measure reserve and study its relation with external variables
    • And especially to look at relations of Memory components with external variables
    • Memory components work better as independent variables

More Detail on Estimating Relations with External Outcome

  • Appendix 1 (from Reed et al., 2010)