Multiple Indicator Growth Models aka, 2 nd Order Growth Daniel E Bontempo Scott M. Hofer. Acknowledgements. Funded in part by Grant R13AG030995-01A1 from the National Institute on Aging
Friday Harbor Psychometrics Workshop 2010
Each model has two latent factors
Growth model has fewer indicators because the latent growth factors cross load
In the factor model the loadings are estimated to get the best factor
In the LGB the loadings ares specified to get a GF corresponding to a specific pattern f growth
MBut WAIT! - Is the indicator reflective?The Nature and Direction of Relationships Between Constructs and Measures: Reflective vs Formative
Edwards, J. R., & Bagozzi, R. P. (2000). On the nature and direction of relationships between constructs and measures. Psychological Methods, 5(2), 155-174.
Presence/severity of cerebrovascular disease
Presence/severity of cardiovasuclar disease
Presence/severity of muscular-skeletal disease
Presence/severity of cancer & immune system related problems
Activity limitationExample: Activity-Limiting Illness
Evidence for measurement invariance involves a nested sequence of increasingly stringent tests (Meredith,1993; Meredith & Horn, 2001).
Configural (Baseline) – intercepts, loadings, & uniquenesses are freely estimated across groups, with minimal constraints only for identification
Weak – constrain factor-variable regressions (i.e., loadings): factor variance in common metric
Strong – constrain intercepts: factor means in common metric
Strict – constrain uniquenesses (i.e., residuals): manifest scores comparableHierarchy of FI Tests
Invariance entails comparable parameters across groups.
1. Strong or Strict Factorial Invariance established
2. Factor-level covariances and means are fixed to zero
3. Metric for LGC parameters is identified by either of two approaches