SOA Norms Report

  1. Introduction
  2. Collecting the Raw Data
    1. ARIC
    2. GMBI
    3. NACC
    4. MCSA
  3. Summarizing the Raw Data
    1. Demographics
    2. Instruments
  4. Generating the Normative Samples
    1. ARIC
    2. GMBI
    3. NACC
    4. MCSA
    5. Pooled
  5. Summarizing the Normative Data
    1. Demographics
    2. Instruments
    3. Groups by Instruments in the Pooled Sample
  6. Generating Instrument Level Models
    1. Notes on the Trail Making Tests
    2. A Note on the LDST
  7. Generating Domain Level Models
  8. Generating Algorithmic Classifications

Generating Instrument Level Models

An instrument level model lets us compute an instrument level z-Score for a SOA participant using the following idea: \[ \text{Instrument Level z-Score} = \frac{( \text{Observed} \text{ Score} \text{ for } \text{ an } \text{ Instrument}) - ( \text{Expected} \text{ Score} \text{ for } \text{ an } \text{ Instrument}) }{\text{RMSE}} .\] Here, the "Expected Score for an Instrument" is a prediction from a linear regression model , while "RMSE" is the Root Mean Square Error for that linear regression model. Details are given below.

Linear Regression Model

The outcome for the linear regression model mentioned above is a SOA instrument (e.g., animals, vfl, etc.). The training sample for the model is a normative sample (e.g., Pooled, ARIC, GMBI, NACC, or MCSA). The predictors for the model are age, sex, race (black or not), education (less than High School, High School, High School or greater). The model includes interaction terms for sex-by-education and race-by-education.

For example, we may fit a linear regression model for the animals instrument based on the NACC normative sample with the following Stata code: 

regress animals age female black##i.edu3cat female##i.edu3cat if weight_NACC == 1

Representing an Instrument Level Model

Since the calculation of an instrument level z-Score depends on the prediction from a linear regression model as well as the RMSE for that model, a complete instrument level model is represented by a collection of Beta Coefficients and a RMSE.

Generating Instrument Level z-Scores

To compute an instrument level z-Score for a participant, we need (i) an instrument level model, (ii) a participant's observed score for that instrument, and (iii) the demographic predictors corresponding to the linear regression model (e.g., age, sex, race, education).

  • We use the demographic predictors and the linear regression model to compute the expected score for the instrument.
  • We subtract the observed score by the expected score.
  • We divide the difference by the RMSE for the linear regression model.