1. Measurement: A Rasch Analysis of Malaysian Automotive Quality Management-Cost of Quality Scale (MAQM-CoQ Scale)
Muhammad Shahar Hj Jusoh , PhD
Rushami Zien Yusoff, PhD
Mohammad Harith Amlus, PhD
Mohd Salleh Hj Din, PhD
Azrilah Abdul Aziz, PhD
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

2. Structure of Discussion
Overview of Measurement
Rasch Model
Instrument Construct
Findings and Discussion
Summary Statistics
Principal Component Analysis (PCA) & Misfits Data
Person-Item Map
Characteristic Curve
Causal Relationship Effect
Conclusion
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

3. Overview of Measurement
Theory of Scales of Measurement (S.S.Stevens, 1946)
Law of comparative judgment (Thurstone,1952)
Scaling and measurement (Guttman, 1950;1954)
Scientific measurement- Thurstone (1952)
Estimation of person and item parameters (Rasch, 1961;1968 & Andersen, 1977)
Inference- Wright (1998)
Additive conjoint measurement- Preece (2002)
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

4. Introduction to Rasch Model
Rasch offers a new paradigm in 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.
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

5. Why Rasch Model ? 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.
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

6. Why Rasch Measurement Model ?
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.
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

7. Why Rasch Measurement Model ?
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.
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

8. Difficulty of a given task
Rasch Measurement Model Theorem
Two (2) propositions appears:
1. Persons who are more able / more developed
have a greater likelihood of correctly answer
all the items / able to complete a given task.
2. Easier items / task are more likely to be
answered correctly by all persons.
In summary:
Person Ability
Pr (Success )
Difficulty of a given task = -
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

9. Rasch Measurement Model Theorem
The Rasch Model incorporates an algorithm that
expresses the probabilistic expectations of an
item ‘i’ and person ‘n’ performances:
Pni(xni=1 | n , i ) =
e(n – i )
1 + e (n – i )
where:
Pni(xni=1 | n , i ) is the probability of person n
on item i scoring a correct response (x=1);
given the person ability, n and item difficulty, i .
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

10. Introduction to Rasch Measurement Model
R E Q U I R EM E N T O F
M E A S U R E M E N T
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 ?
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

11. Rasch Model ‘logit’ scale
In Rasch Model, a turn of event is seen as a chance; a likelihood of happenings hence a ratio data.(Steven, 1946) 10 90
10-2 -2 30 70 60 40 50 99 1
100
102 2 -1
exp
logit
Now, we already have a SCALE with a unit termed ‘logit’.
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

12. Rasch Analysis Capabilities
INSTRUMENT RELIABILITY
RESPONSE VALIDITY
CALIBRATION
PRINCIPAL COMPONENT
ANALYSIS (PCA)
QUALITY CONTROL
QUANTITATIVE
- S.D, Cronbach’s-α, Mean, Z-test
PREDICTIVE MODEL
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

13. Finding 1: Summary Statistics
Bond and Fox (2007) and Fisher Jr. (2007), analyzing the summary statistic is the essential steps in determining the reliability, validity, consistency and significance issues during the item construct processes. In the Rasch’s summary statistic, prescribes of all the necessary statistical features of sufficient details to represents and answers the goodness of data issues such: reliability, validity, consistency and significance.
- Summary Statistics Table
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

14. Finding 1: Summary Statistics
-ve Person mean
μ = logit
P[Ɵ] LOi=
0.66 ‘Poor’ Person separation of 2 groups.
0.31 ‘Poor’ reliability
Valid Responses:
99.9%
Cronbach-α :0.33 Poor reliability assessment of student learning
0.99; ‘Very Good’ instrument reliability in item measuring student learning ability
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

15. Finding 1: Summary Statistics
1. Validity
Measuring what is supposed to be measured in the right hierarchy (Wright & Stone, 1979; Linacre , 2004).
Item reliability will suggest proven evidence on the item difficulty hierarchy is the best terminology to represent the understanding of validity in instrument construct (Andrich, 1988; Bond & Fox, 2007; Fisher, 2007; Linacre, 2008).
Validity has no meaning by itself but is useful tools for crafting a variable and defining its numerical properties (Wright & Stone, 1979).
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

16. Finding 1: Summary Statistics
2. Reliability
Person reliability used a linear interval scale (when the data fit the model requirements) compared with a usually nonlinear raw score scale used in the calculation of KR-20 (Schumacker & Smith. Jr., 2007).
Need to be deliberated by the person separation index as well (Andrich, 1988; Linacre, 2008; Pagani & Zanarotti, 2008; Fisher. Jr. et. al, 2010).
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

17. Finding 1: Summary Statistics
3. Significance
How high must the probability be before an investigator is willing to declare that a relationship between variables exists (Ary et.al., 2002) or “the statements that have high probability of being correct rather than an absolute truth statements”.
The applicable level of significance test is set at 0.05 level where the Z-standard (normal curve) condition acceptable range is within -2 < Z < +2 in two-tailed test (Andrich, 1988; Bond & Fox, 2007; Fisher, 2007; Linacre, 2008).
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

18. Finding 2: PCA & Quality Control
Yen (1993) and Zenisky, et al. (2003) suggested using the local item dependence to detect dependency between pairs of items or persons.
Wright (1999), share more than half of their random variance suggesting that only one of these two items is needed for measurement (one of the items have to be discarded or removed).
Local dependence would be large positive correlation, with highly locally dependent items (Correlation > 0.7) suggesting that only one of the two items is needed for measurement based table Principal Component Analysis : Largest Standardized Residual Correlations (Wright et al.,2003).
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

19. Finding 2: PCA & Quality Control
4 criteria as to check for any outliers or misfits data, as any misfits pattern to be considered are focused on the requirements given, that are:
1) Point Measure Correlation (PT-Mea Corr); 0.4 < PT-Mea Corr value < 0.85.
2) Point Measure Correlation (PT-Mea Corr); gave a negative value (meaning that the person expected to be misfit due to careless respond or guessing or the
given pattern is reverse than the ideal pattern).
3) Outfit Mean Square (MNSQ); 0.5 < Outfit MNSQ value < 1.5
4) Outfit Z-Standard (Z-STD); -2 < Outfit Z-Std value <+2
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

20. Finding 3: Person-Item Map
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

21. Finding 4: Characteristic Curve
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

22. Finding 5: Causal Relationship Effect
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

23. Novelty Developed the measurement ‘ruler’ Measurement Standard
Transform ordinal into equal interval scale
Measure item or tasks difficulty
Measurement Standard
Meet the standard hence measurement requirement
Validation of instrument construct
Better reflect measure of ability
Precision and Accuracy of measurement.
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

24. 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 operational management research via longitudinal research; clearer to read, easy to understand.
2nd International Postgraduate Conference on Business Management (IPCBM 2016), February 2016, Pulau Langkawi

25. Thank you. Any Q ?