﻿ Decimal and continuous data

# Decimal and continuous data

Facets expects the data to be in the form of integers. Ascending integers are taken to represent a hierarchical order of qualitatively more of whatever is being observed. Each higher integer means one more level of the latent variable.

Averaged data: Example: For one element, the data looks like 2.7, 5.6, 8.9, ranging from 0 to 10. but other items are integers.
In Facets, every advancing score must mean one higher level of the latent variable. In your data, 0,1,2,3,4,5,6,7,8,9,10  are 11 levels of performance.

What does 2.7 mean?  From the viewpoint of Facets it means:

an observation of 2 weighted 0.3 (= 0.6) + an observation of 3 weighted 0.7 (= 2.1 so that 0.6+2.1=2.7)

so, if the original Facets observation was:

facet1, facet2, facet3, 2.7

then the Facets data is:

Data=

R0.3, facet1, facet2, facet3, 2

R0.7, facet1, facet2, facet3, 3

Decimal data due to intermediate levels: Example: performances are scored in increments of 0.5, e.g., 2.0, 2.5, 3.0.

Multiply the observations by whatever is required to put them into integer form, or use the Rating scale= specification to recode the data. For performances scored in increments of 0.5, e.g., 2.0, 2.5, 3.0. Multiply the observations by 2 for analysis: 4, 5, 6. To maintain the original raw scores, weight these by 0.5:

Model = ?,?,?,R6, 0.5

Example: The performances have ratings like 3.5, but Facets expects integers.

A. Convert the observation from 3.5 to 7:

Rating scale = Wscale, R10

7 = ,,, 3.5 ; convert 3.5 into 7

..... ; and all the other possible observations

*

B. Weight the observation by a half

Models=?,?,?,Wscale,0.5 ; Weight the model 0.5

Continuous data: chunk this up into qualitatively advancing pieces and number the chunks in ascending order. For instance, a timed task in which shorter time is better. 0.0-0.5 seconds = 6; 0.5-1.5 seconds = 5, 1.5-3.0 seconds = 4, 3.0-6.0 seconds = 3, etc. This recoding can be done with Rating scale=.

Rating scale = Tscale, R6

6 = ,,,  0.0+0.1+0.2+0.3+0.4+0.5 ; convert 0.0-0.5 into 6

56 = ,,,  0.6+0.7+0.8+0.9+1.0+1.1+1.2+1.3+1.4+1.5 ; convert 0.5-1.5 into 5

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Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments, George Engelhard, Jr. & Stefanie Wind Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
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