xni = 0,1,2,3,,,K
maximizes residual noise
minimizes residual noise
| COMPARING FACTOR ANALYSIS AND RASCH MEASUREMENT | ||
|---|---|---|
| ASPECT | FACTOR ANALYSIS | RASCH MEASUREMENT |
| Motive | summarize data | construct measurement |
| Input Model | "linearities" | stochastic events |
| Missing Data | loses rows or columns, biases factors | routinely accommodated, no data lost |
| Co-mensuration | norm-standardized into "linearities" |
criterion-classified into ordered categories xni = 0,1,2,3,,,K |
| Method | principal components (or common factor) | latent trait |
| Model | |
|
| Estimated by Minimizing | |
|
| Anchored at | |
|
| Error Model | |
|
| Item Estimate | vi regression of factor score un on item i | Di linear calibration of item i on variable |
| Item Estimate Error | |
|
| Person Estimate | un score predicted for person n on factor | Bn linear measure of person n on variable |
| Person Estimate Error | |
|
| Residual Statistics | |
|
| Misfits | |
|
| To Seek Next Variable | subtract unvi from all zni for next data maximizes residual noise |
select only xni of misfitting items minimizes residual noise |
Benjamin D. Wright 1994 RMT 8:1 p. 350
Comparing factor analysis and Rasch measurement Wright BD. … Rasch Measurement Transactions, 1994, 8:1 p.350
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