Structure of Discussion : Structure of Discussion Overview of Measurement
Rasch Model
Instrument Construct
Findings and Discussion
Summary Statistics Observations
Person-Item Map
Item Analysis
Item Bank
Conclusion
Introduction to Rasch Measurement Model : Introduction to Rasch Measurement Model Rasch offers a new paradigm in research.
Rasch is a probabilistic model that offers a better method of measurement construct hence a scale.
Rasch gives the maximum likelihood estimate (MLE) of an event outcome.
Rasch read the pattern of an event thus predictive in nature which ability resolves the problem of missing data. Hence, more accurate.
Why Rasch Measurement Model ? : Why Rasch Measurement Model ? Data is ordinal; and small sample size.
Easy to read, clearer to understand results.
An instrument with scalar properties.
Instrument is independent of sample.
The Theory Behind : The Theory Behind Danish Mathematician Georg Rasch (1960) constructed the necessary and sufficient mathematical model for the transformation of ordinal observations into linear measures.
is form of a logistic regression model, but each person and item is individually parameterized coefficient applied to a dummy variable.
The Theory Behind : The Theory Behind Standard Rasch model for dichotomous data with persons and items is expressed as:
P(Ɵ) = log ( Pni/(1-Pni))
where Pni is the probability that person n will succeed on item i, where person ‘n’ has ability Bn and item ‘i ‘has difficulty Di.
Giving Probability of Success as;
P(Ɵ) = Bn – Di
Model is additive in the parameters (Bn) and (Di)
The Theory Behind : The Theory Behind It meets the first requirement for interval measurement.
Maximum-likelihood of the parameter estimate for each parameter occurs when the expected raw score corresponding to the parameter estimate equals the observed raw score.
Thus, it fulfill Fisher's Principle (1913) of statistical sufficiency.
The Theory Behind : The Theory Behind A difference..
Statistician believe data points tell the truth and that it is the task of statisticians to find models which explain them and to find the latent/hidden variables which underlie them ; best fit line.
Rasch Model believe latent variable is the truth, and when that latent variable is expressed in linear terms.
Rasch looks at how best the data fits the model instead.
Rasch Model hybrids : Rasch Model hybrids extended to rating scale, say Likert or Guttmann while maintain the same mathematical properties :
Polytomous model (Andrich, 1978)
log ( Pnijk/Pnij(k-1)) = Bn - Dgi - Cj – Fgk
(note: Cj and Fgk is extended measurement)
supports powerful quality-control fit statistics for assessing the conformance of the data (robust against misfit)
plots of the measures do have the geometric properties generally assumed by unsophisticated readers to exist in all numbers.
estimation perspective under JMLE, anchored and unanchored items appear exactly alike
Rasch Model hybrids : Rasch Model hybrids Further extended to Partial Credit Model for multiple rating used (Masters, 1982)
This is to handle evaluation having multiple ratings; (0,1) , (1,2,3,4) , (1 2 3 4 5 6 7) etc.
Most advanced is the Multi Faceted Rasch Model (MFRM) [Linacre, 1992] to handle cases of multiple raters instead.
estimation perspective under JMLE, anchored and unanchored items appear exactly alike
Rasch Model thus… : Rasch Model thus… provides a mathematical framework against which we can compare data
converts dichotomous and rating scale (ordinal) observations into linear quantifiable measures
links qualitative analysis to quantitative methods on line of linear enquiry.
useful measurement involves examination of only one human attribute at a time (uni-dimensionality)
Introduction to Rasch Measurement Model : Introduction to Rasch Measurement Model WHAT IS THE INSTRUMENT USED?
WHAT IS THE UNIT OF QUANTITY?
WHAT IS THE SCALE CONSTRUCT?
IS IT OF LINEAR EQUAL INTERVAL?
IS THE MEASURE REPLICABLE?
IS IT PREDICTIVE ? R E Q U I R EM E N T O F
M E A S U R E M E N T
Introduction to Rasch Measurement Model : D E F I N I T I O N OF
M E A S U R E M E N T RASCH MEASUREMENT MODEL IS ABLE TO MEET ALL THESE
R E Q U I R E M E N T S Introduction to Rasch Measurement Model
Introduction to Rasch Measurement Model : 14 selected persons and 12 selected items Introduction to Rasch Measurement Model
Slide 14 : Introduction to Rasch Measurement Model Person Rank Order
Slide 15 : Introduction to Rasch Measurement Model
Slide 16 : Student.1: 1. But, atypical test result tabulation only rank the students from the highest score in descending order 2. Need to assess beyond raw score. Rasch sorts further according to response pattern in descending order; modified called ‘Rasch-Guttman scale’. Student.7: S-03: S-05: Introduction to Rasch Measurement Model
Slide 17 : Rasch Measurement Model Theorem SMART POOR RESPONSE
SORTED: EASY TO TOUGH Student.01 S-02 S-03 S-04 S-05
Slide 18 : Rasch Model Probability Expression; P(Ɵ) βn= ability POOR Student.01 S-02 S-03 S-04 S-05
Slide 19 : Andrich-Rasch Polytomous (1978) RESPONSE
SORTED: EASY TO TOUGH
Slide 20 : Masters Partial Credit Model (1982) RESPONSE
SORTED: EASY TO TOUGH
Slide 21 : Linacre, Multi-Facet Rasch Model(1992) RATER 1 RATER 2 RATER 3 ST 1- ST 2- ST 3- ST 4- ST 1- ST 1- ST 5- ST 8- ST 7-
Slide 22 : 8:18 AM 22 Measurement Overview:
- Q & A Session
: What is an instrument construct ?
Rasch Model ‘logit’ scale : e.g. On a graduation day, what is the likelihood of a lady liking
to a piece of rose as your giving ? Perhaps 30:70
Compare if you send a bouquet instead. It increases to 60:40; and so forth if you put a Fererro Roche.. the chances gets better. In Rasch Model, a turn of event is seen as a chance; a likelihood of happenings hence a ratio data.(Steven, 1946) Now, we already have a SCALE with a unit termed ‘logit’. Rasch Model ‘logit’ scale
Introduction to Rasch Analysis : Introduction to Rasch Analysis INSTRUMENT RELIABILITY
RESPONSE VALIDITY
CALIBRATION
QUALITY CONTROL
QUANTITATIVE
S.D, Cronbach-α, µ, z-Test, PCA
PREDICTIVE MODEL
Finding 1: Summary Statistics : 0.99; ‘Very Good’ instrument reliability in item measuring student learning ability Finding 1: Summary Statistics Valid Responses:
99.9% -ve Person mean
μ = -0.03 logit
P[Ɵ] LOi= 0.4921 0.66 ‘Poor’ Person separation of 2 groups.
0.31 ‘Poor’ reliability Cronbach-α :0.33 Poor reliability assessment of student learning
Finding 2: Person-Item Map : Finding 2: Person-Item Map 1. Poor Students; n=139 (57.20%) 2.Good students; n=104 (42.80%)
Finding 3: Item Person Measure : Finding 3: Item Person Measure VERY DIFFICULT
= +1.82logit
N=243, score=329
ave.=1.35, many cannot do EXTREMELY EASY
=-7.42logit
N=243, score=1215
ave.=5, all correct ITEM SD=2.5
PERSON SD=0.48
ITEM OFF TARGET BOTH y,z BREACHED ITEM NEED REVIEW -2 < Z < +2 0.5 < y < 1.5 Large +Z due to inconsistency in response. e.g.Poor Person can answer difficult questions 0.32 < x< 0.8 LOW PT. MEASURE CORELATION . SOME POOR STUDENTS CAN ANSWER ITEMS CORRECTLY WHILST GOOD STUDENTS GOT WRONG
Finding 4: Item Misfit Response String : Finding 4: Item Misfit Response String Most misfit item:
Exceed MNSQ Limit: 0.5 < y < 1.5
Finding 5: Predictive Model : Finding 5: Predictive Model High Rating Response Zone 5 – 3. Item in red circles for the respective Persons were under rated
Novelty : Novelty Developed the measurement ‘ruler’
Transform ordinal into equal interval scale
Measure item or tasks difficulty
Measurement Standard
Meet SI unit standard hence measurement requirement
Validation of instrument construct
Better reflect measure of ability
Precision and Accuracy of measurement.
Conclusion : Conclusion Rasch probalistic model offers an better method to verify the validity of a measurement construct hence precision.
Rasch predictive ability resolves the problem on the need of students taking all the tests; Rasch estimate the likely responses based on anchored items.
Rasch gives the maximum likelihood estimate (MLE)
of an event outcome.
Rasch offers a new paradigm in education/ research; clearer to read, easy to understand.
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