Rasch Model Theorem_Scale Construct

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  • 44
  • Rasch Model Theorem_Scale Construct

    1. 1.  Overview of Measurement Rasch Model Instrument Construct Findings and Discussion ◦ Summary Statistics Observations ◦ Person-Item Map ◦ Item Analysis ◦ Item Bank Conclusion
    2. 2.  Rasch offers a new paradigm in education longitudinal 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.
    3. 3. What are the advantages of doing a Rasch analysis? Results easy to read and clearer to understand A parameter estimate (personal profile) for each of the individuals from the data. Comparisons between individuals become independent of the instrument used. Comparisons between the stimuli (items) become independent of the sample of individuals.
    4. 4. These leads to: Probabilistic models. Separability of parameters. Parameterization in a multiplicative or additive frame-of-reference. Evaluation of the goodness of fit of the data to the models.
    5. 5. When do you need Rasch analysis? Data in hand is ordinal hence qualitative; but study requires quantitative analysis. Study call for correlation of items. Sample size dealt with is small. A valid scalar instrument of measurement.
    6. 6. R E Q U I R EM E N T O F MEASUREM ENT• 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 ?
    7. 7. D E F I N I T I O N OF MEASUREM ENTRASCH MEASUREMENT MODEL IS ABLE TO MEET ALL THESEREQUIREMENTS
    8. 8. 1. But, atypical test result tabulation only rank the students from the highest score in descending order Q1 Q15 Q16 Q30 Q31 Q50 111111111111001 = 10111011111111111Student.1: 11111111111111111 48 111111111011111 = 1010010001111111 11111111111111111 43 10111111111111111 S-03: 1110111111100100 01101010001101 = 33 10111111111011111 1111111111010100 10110100000011 = 33 10110111111111111 S-05: 1011111101001110 00010000100001 = 33 10111111111111111 111101100100010 01000000000001 = 27Student.7:10111111111111101 110101000100010 00000000001001 = 24 2. Need to assess beyond raw score. Rasch sorts further according to response pattern in descending order; modified called ‘Rasch-Guttman scale’.
    9. 9. Theorem 1. Persons who are more able / more developed have a greater likelihood of correctly answer all the items / able to complete a given task. EASY ITEMS DIFFICULT ITEMS SMART Q3 Q1 Q7 Q5 Q4 Q2 CARELESSStudent.0111111011111111111 11111111111111111 111111111110110 = 48 111111111 1111111 11111111111111111 11111001000010 = 43 PREDICT=1 S-0311111111111111111 1111011011110010 11101010000000 = 33 S-0411111111111111111 0111101111011101 10110100000000 = 33 S-0511010110111101111 1011111101001101 10110110101110 = 33 REVERSED 11111111111111010 0111011101000100 0100 000001000 = 27 PREDICT=0POOR S-02 11111111111111101 1101110100100100 00000000001000 = 24 RESPONSE SORTED: 7 6 5 4 3 GUESS 0 EASY TO Theorem 2. Easier items / task are more likely to be TOUGH answered correctly by all persons.
    10. 10. 1. Persons who are more able / more developed have a greater likelihood of correctly answer all the items / able to complete a given task. δi =ITEM DIFFICULTYβn= ability Q3 Q1 Q7 Q5 Q2Student.01 11111011111111111 11111111111111111 111111111110110 = 48 111111111 1111111 11111111111111111 11111001000010 = 43 e (βn – δi ) S-03 11111111111111111 1111011011110010 P(Ɵ 11101010000000 = 33 )= S-04 11111111111111111 0111101111011101 1 + e (βn – δi ) 10110100000000 = 33 S-05 where; 11010110111101111 1011111101001101 10110110101110 = 33 e= Euler’s Number, 2.7183POOR S-02 11111111111111010 0111011101000100 β Person’s ability measure n= 0100 000001000 = 27 11111111111111101 1101110100100100 00000000001000 = 24 δi= item difficulty measure 2. Easier items / task are more likely to be answered correctly by all persons.
    11. 11. zrilah@gmail.com
    12. 12. zrilah@gmail.com
    13. 13. Measurement Overview:- Q & A Session: What is an instrument construct ? 06:49 AM 13
    14. 14. In Rasch Model, a turn of event is seen as a chance; a likelihood of happenings hence a ratio data.(Steven, 1946) 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. 1 10 30 50 60 99 99 90 70 50 40 1 10-2 100 102explogit -2 -1 0 1 2 Now, we already have a SCALE with a unit termed ‘logit’.
    15. 15. • INSTRUMENT RELIABILITY• RESPONSE VALIDITY• CALIBRATION• QUALITY CONTROL• QUANTITATIVE  S.D, Cronbach-α, µ, z-Test, PCA• PREDICTIVE MODEL
    16. 16. -ve Person mean μ = -0.03 logit P[Ɵ] LOi= 0.49210.66 ‘Poor’ Personseparation of 2 groups.0.31 ‘Poor’ reliabilityValid Responses:99.9%Cronbach-α :0.33 Poorreliability assessmentof student learning0.99; ‘Very Good’instrument reliabilityin item measuringstudent learning ability
    17. 17. 2.Good students; n=104 (42.80%)1. Poor Students; n=139 (57.20%)
    18. 18. VERY DIFFICULT= +1.82logitN=243, score=329 0.5 < y < 1.5 -2 < Z < +2 Large +Z due to inconsistencyave.=1.35, many in response. e.g.Poor Personcannot do can answer difficult questions BOTH y,z BREACHED ITEM NEED REVIEW ITEM SD=2.5EXTREMELY EASY PERSON SD=0.48=-7.42logit 0.32 < x< 0.8 ITEM OFF TARGETN=243,score=1215 LOW PT. MEASURE CORELATION .ave.=5, all correct SOME POOR STUDENTS CAN ANSWER ITEMS CORRECTLY WHILST GOOD STUDENTS GOT WRONG
    19. 19. Most misfit item:Exceed MNSQLimit: 0.5 < y < 1.5 High Rating Response Low Rating Response Zone 5 – 3. Item in red Zone 3 – 1. Item in blue circles for the respective circles for the respective Persons were under rated Persons were over rated
    20. 20. High Rating ResponseZone 5 – 3. Item in redcircles for the respectivePersons were under rated
    21. 21. 1. Developed the measurement ‘ruler’ ◦ Transform ordinal into equal interval scale ◦ Measure item or tasks difficulty2. Measurement Standard ◦ Meet SI unit standard hence measurement requirement3. Validation of instrument construct ◦ Better reflect measure of ability ◦ Precision and Accuracy of measurement.
    22. 22.  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 engineering education longitudinal research; clearer to read, easy to understand.
    23. 23. aidfudin@gmail.com 60 12240 2821

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