Rasch analysis of the RolandMorris Disability Questionnaire

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Rasch analysis of the Roland-Morris Disability
Questionnaire

• Megan Davidson, PhD
• School of Physiotherapy,
• La Trobe University, Melbourne

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Questionnaires

• Functioning
• Disability
• Ability
• Health status
• Activity limitations
• Participation restrictions
• Quality of life
• Well being
• Level of assistance

• Typically have n items summed to give a total
  score
• Higher score indicates more or less of the
  thing being measured

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The scores are ordinal

• Rank order
• Distance between ranks is unknown
• Distance between adjacent scores are not
  equivalent units
• Arguably, ordinal scores cannot be manipulated
  mathematically

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How far will the cars go?

• 4 cars are filled with petrol to see how far they
  go on a full tank of fuel.
• 3 observers are positioned along the route.

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Green Score 3 Blue Score 2 Red Score
2 Yellow Score 1
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Rasch analysis

• Modern Test Theory (Item response)
• Models the probability that a person of ?
  ability will be able to do activity of d
  difficulty
• Locates item difficulty and person ability on an
  interval-level logit scale
• Logit log-odds unit
• probability a person can perform the task divided
  by the probability they cannot

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Advantage of Rasch modelling

• Measure what is measurable, and make measurable
  what is not so. (Galileo Galilei)
• Rasch provides an operational criterion for
  fundamental measurement of the kind found in the
  physical sciences David Andrich

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Easy activities
Hard activities
Get out of bed
Housework
Gardening
Sport
Least able person
Most able person
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Roland-Morris Questionnaire (RDQ)

• A low-back specific disability questionnaire
• 24-items from the Sickness Impact Profile
• Patient self-completed
• Tick those that apply today
• Number of items selected score
• Possible score 0-24
• Higher score indicates greater disability

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Roland-Morris Disability Questionnaire

• I stay at home most of the time because of my
  back
• I change position frequently to try and get my
  back comfortable
• I walk more slowly than usual because of my back
• Because of my back, I am not doing any of the
  jobs that I usually do around the house

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RDQ content

• housework
• self-care
• walking
• sleeping
• sitting
• irritability
• appetite
• pain

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Short-form versions RDQ

• 18-item version
• Stratford Binkley 1997
• 18-item version
• Williams Myers 2001

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Classical (Traditional) Test Theory

• Reject/retain items on some basis
• Very low or high response frequency
• Very low or high item-item correlations
• Low or high corrected item-total correlations
• Cronbachs alpha in range considered desirable

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18-item versions

• Stratford Binkley
• Response frequency lt20 or gt90
• Item-item correlations gt 0.75
• Item-total correlations lt .40
• Increased Cronbachs alpha

• Williams Myer
• Response frequency lt20 or gt80
• Item-item correlations gt 0.75
• Item-total correlations lt .20
• Cronbachs alpha gt.80

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Items removed in 18-item versions

• Stratford Binkley
• 2 change position
• 15 appetite not good
• 17 walk short distance
• 19 dress with help
• 20 sit most of day
• 24 stay in bed

• Williams Myers
• 2 change position
• 15 appetite not good
• 19 dress with help
• 20 sit most of day
• 22 more irritable
• 24 stay in bed

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Aim

• To examine fit to a Rasch model of the 24-item
  and two 18-item versions of the RDQ
• To explore whether decisions to reject items on
  the basis of Rasch analysis would differ from
  that made by the developers of two 18-item
  versions of the RDQ.

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Is RDQ unidimensional?

• Items drawn from several SIP domains
• Williams Myers 2001
• Many low item-item and some low item-total
  correlations
• 4 factors explaining 55 of total variance

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Method

• Data for 140 people from a previous study
• Battery of questionnaires including RDQ
• Participants were seeking physiotherapy treatment
  for a low back problem
• aged 18 years or older
• read and write English.
• Recruited from public hospitals, community health
  centres and private practices.
• RUMM2020 Rasch analysis software

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Results (n 140)

• Mean age 51 years (sd 17, range 18-89)
• 66 female
• 41 employed
• 43 pain lt 6 weeks
• 34 pain gt 6 months
• 70 pain that referred into the buttock or leg.
• RDQ score 9 (sd 5.6), median 8 (IQR 5-14).

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COMPARISON OF FIT TO THE RASCH MODEL
Poor fit if item-trait p lt.05, item residual gt
2, ?2 p lt .01, F p lt .01 PSI Person Separation
Index
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Differential Item Functioning (DIF)

• An item may attract systematically different
  responses on the basis of some characteristic
  other than item difficulty
• Age
• Gender
• DIF by age and gender in all versions
• Item 5 Because of my back, I use a handrail to
  get upstairs

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Which items would Rasch reject?

• 17 walk short distances
• 9 dress slowly
• Negative residuals indicate redundancy
• 5 use handrail upstairs
• DIF by age/gender
• 16 trouble putting on socks
• DIF by age, another item at same location on
  logit scale

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20-items fit the Rasch model

• Item-Trait interaction
• Total item chi square gt .05 p .424
• Item Fit
• Item residuals all lt 2.0
• Item Chi Square and F-stat all p gt.01
• No DIF by age and gender
• PSI 0.83

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Items removed

• Stratford Binkley version 2,15,17,19,20,24
• Williams Myers version 2,15,19,20,22,24
• Rasch 21-item version 5,9,16,17

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24-item RDQ Targetting
21 avoid heavy jobs -2.35
19 dress with help 4.12
Increasing item difficulty Increasing person
ability
Decreasing item difficulty Decreasing person
ability
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24-item RDQ Targetting
gap
gap
gap
cluster
Decreasing item difficulty Decreasing person
ability
Increasing item difficulty Increasing person
ability
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24-item RDQ
19 Dress with help
17 Walk short distances
2 Change position frequently
24 Stay in bed 15 Appetite not good 20 Sit most
of the day
18-item RDQ Stratford
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24-item RDQ
18-item RDQ Williams
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24-item RDQ
20-item Rasch selection
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Raw Scores Vs Rasch Measure
Change of 5 points from 10 to 5 1.16 logits
Change of 5 points from 5 to 0 2.58 logits
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Conclusions

• Traditional and Modern Test Theory approaches
  reject different items
• Rejecting items of very low/high frequency
  results in truncated scale
• RDQ can be made to fit Rasch model, but
  targetting is poor
• Gaps in item difficulty locations
• No items of sufficient difficulty for high
  ability persons

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Rasch Group Meeting Swinburne Hawthorn Monday 5th
Dec, 4.00pm Room AR103 Graduate School of
Research (next door to Haddons coffee shop in
campus centre) Megan Davidson m.davidson_at_latrobe.
edu.au Julie Pallant JPallant_at_groupwise.swin.edu.
au