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Creating Valid and Effective Measures Using –optifact- to Create Better Summated Rating Scales North American Stata Users' Group Meetings Boston, July 11-12, 2005

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Are measures important? Measures are how theory is translated into data for modeling Unlike art, where we want to engage individual interpretation as a major component of the work Measures need to be unambiguously interpreted in precisely the same way by all

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Why Scales? Combining the results of several questions is more reliable and precise, and reduces measurement error (Spector, 1992)

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What makes a good scale? It is reliable The same measurement, produces similar results across time and persons The questions or items that make up the scale are consistent with one another It is valid It measures the concept that it is intended to measure It measures one concept It is regularly distributed

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Reliability Internal Reliability Internal consistency: the items should inter- correlate (Cronbach’s Alpha) Test-Retest Reliability Same measure taken again should produce consistent results

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Validity Rationale The items must be consistent with theory and the concept under consideration Criterion Validity The items should vary in the same way to other variables that are theoretically related to the concept Canonical correlation

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Uni-dimensional, Efficient Scales that measure a single concept are more useful in establishing causal relationships Efficient scales use only enough items to reliably measure a concept Regular distributions allow standard modeling techniques

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Research Question If my scales are not uni-dimensional, are there sub-scales which are and meet the criteria associated with good scales? Investigated using data gathered for the Canadian National Longitudinal Survey of Children and Youth by Statistics Canada.

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Data and Method The NLSCY cycles 1, 2 and 3 Measures on parenting and child behaviour taken every two years (allows the investigations of test- retest reliability) N > 13,000. Common factor analysis Dimensions, alpha Canonical correlation Criterion validity

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Problems There are a lot of candidate scales 2 k – 1, if scales of all sizes are considered The testing procedure is lengthy Factor analysis (dimensionality) Alpha (internal reliability) Canonical Correlation (external validity) Re-test (all of the above, twice) More than 13 scales

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Solution: optifact A Stata software component to analyze a list of candidate items for the creation of a summated rating scale

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-optifact- Specification optifact varlist [weight] [if exp] [in range] [, top(#) smallest(#) largest(#) maxfact(#) minslope(#)] Varlist: the list of candidate items (numeric) Options: Top: the number of candidate scales to list (10) Smallest: the smallest k allowed (3) Largest: the smallest k allowed (all items) Maxfact: the maximum number of factors allowed (1)

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-optifact- Output optifact abecq6b abecq6n abecq6w abecq6p abecq6i abecq6qq abecq6hh abecq6s [aweight=awtcw01c], top(20) criteria(childsex ammcq01) 8 items will be processed There are 219 potential scales 56 combinations of 3 items had one factor, 0 had more than one factor Top 5 scales using 3 items Avg. Can K Alpha Cov. Chk Items Yes abecq6p abecq6i abecq6qq Yes abecq6p abecq6i abecq6hh Yes abecq6b abecq6n abecq6hh Yes abecq6p abecq6qq abecq6hh Yes abecq6n abecq6p abecq6i 55 combinations of 4 items had one factor, 15 had more than one factor Top 5 scales using 4 items Avg. Can K Alpha Cov. Chk Items Yes abecq6p abecq6i abecq6qq abecq6hh Yes abecq6n abecq6p abecq6i abecq6hh Yes abecq6n abecq6p abecq6i abecq6qq Yes abecq6b abecq6p abecq6i abecq6hh Yes abecq6p abecq6i abecq6qq abecq6s

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Behaviour Scales VariableConceptskAlpha Hyperactivity (becs06) Prosocial Behaviour (becs07) Emotional Disorder /Anxiety (becs07) Aggression (becs Indirect Aggression (becs10) Property Offences (becs11)

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Parenting Scales VariableConceptskAlpha Positive interaction (0-23 months) (prcs01) Ineffective parenting style (0-23 months) (prcs02) Positive interaction (2-11 years) (prcs03) Ineffective parenting style (2-11 years) (prcs04) Consistency (2-11 years) (prcs05) Rational parenting style (2-11 years) (prcs06) PMK Depression (dpps01)

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Results Of these 13 scales only one was uni- dimensional Most had larger number of items than desirable for the value of alpha

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New Behaviour Scales VariableConceptskAlphaConcepts’k’Alpha’ Hyperactivity (becs06) Prosocial Behaviour (becs07) Emotional Disorder /Anxiety (becs07) Aggression (becs09) Indirect Aggression (becs10) Property Offences (becs11)

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New Parenting Scales VariableConceptskAlphaConcepts’k’Alpha’ Positive interaction (0-23 months) (prcs01) Ineffective parenting style (0- 23 months) (prcs02) Positive interaction (2-11 years) (prcs03) Ineffective parenting style (2- 11 years) (prcs04) Consistency (2-11 years) (prcs05) Rational parenting style (2-11 years) (prcs06) PMK Depression (dpps01)

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Implications These scales are part of a large survey conducted every 2 years in Canada on more than 20,000 children The survey has completed 6 cycles of data collection Each question has been asked more than 120,000 times

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Implications (Cont’d) The scales required 85 questions The revised scales require 30 questions More than 55,000,000 questions

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Caveats Most scales in the NLSCY are not the best that can be made from the available data Some of these scales should not be used The NLSCY is an excellent survey, conducted by competent statisticians Similar results might be expected in other major surveys

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Conclusions -optifact- can help find better measures Uni-dimensional Valid Reliable -optifact- can reduce costs Equivalent or better measure for same money

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