Optifact Summated Scales

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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



Why Scales?

Combining the results of several questionsis more reliable and precise, and reducesmeasurement error (Spector, 1992)



R eliabilit y

I nternal ReliabilityI nternal consistency: the items should inter-correlate (Cronbach¶s Alpha)

Test-Retest Reliability� Same measure taken again should produce

consistent results



U ni-dimensional, Efficient

Scales that measure a single concept aremore useful in establishing causalrelationshipsEfficient scales use only enough items toreliably measure a concept

Regular distributions allow standardmodeling techniques



R esearc h Question

I f my scales are not uni-dimensional, arethere sub-scales which are and meet thecriteria associated with good scales?I nvestigated using data gathered for theCanadian National Longitudinal Survey of

Children and Youth by Statistics Canada.



D ata and Met hod

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



P roblems

There are a lot of candidate scales2 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



Solution: optifact

A Stata software component to analyze alist of candidate items for the creation of asummated rating scale



-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)



-optifact- Output

optifact abecq6b abecq6n abecq6w abecq6p abecq6i abecq6qq abecq6hh abecq6s[aweight=awtcw01c], top(20) criteria(childsex ammcq01)

8 items will be processedThere are 219 potential scales

56 combinations of 3 items had one factor, 0 had more than one factor

Top 5 scales using 3 itemsAvg. Can

K Alpha Cov. Chk Items- ----- ----- --- -----

1 3 0.774 0.201 Yes abecq6p abecq6i abecq6qq2 3 0.769 0.203 Yes abecq6p abecq6i abecq6hh3 3 0.744 0.231 Yes abecq6b abecq6n abecq6hh4 3 0.742 0.169 Yes abecq6p abecq6qq abecq6hh

5 3 0.734 0.213 Yes abecq6n abecq6p abecq6i

55 combinations of 4 items had one factor, 15 had more than one factorTop 5 scales using 4 items

Avg. CanK Alpha Cov. Chk Items- ----- ----- --- -----

1 4 0.802 0.185 Yes abecq6p abecq6i abecq6qq abecq6hh2 4 0.784 0.199 Yes abecq6n abecq6p abecq6i abecq6hh3 4 0.776 0.191 Yes abecq6n abecq6p abecq6i abecq6qq4 4 0.775 0.198 Yes abecq6b abecq6p abecq6i abecq6hh



B ehaviour Scales

Variable Concepts k Alpha

H yperactivity(becs06) 3 8 0.84

Prosocial Behaviour (becs07) 4 10 0.76

Emotional Disorder /Anxiety (becs07) 3 8 0.78

Aggression(becs09 2 6 0.78

Indirect Aggression(becs10) 1 5 0.78

Property Offences(becs11)

2 6 0.62



P arenting Scales

Variable Concepts k Alpha

Positive interaction (0-23months) (prcs01) 2 5 0.73

Ineffective parenting style(0-23 months) (prcs02) 1 2 0.37

Positive interaction (2-11years) (prcs03) 2 5 0.81

Ineffective parenting style(2-11 years) (prcs04) 3 7 0.70

Consistency (2-11 years)(prcs05) 2 5 0.68

Rational parenting style(2-11 years) (prcs06) 2 6 0.62

PMK Depression(dpps01) 4 12 0.82



R esults

Of these 13 scales only one was uni-dimensionalMost had larger number of items thandesirable for the value of alpha



N ew P arenting Scales

Variable Concepts k Alpha Concepts¶ k¶ Alpha¶

Positive interaction (0-23months) (prcs01) 2 5 0.73 1 3 0.63

Ineffective parenting style (0-23 months) (prcs02) 1 2 0.37

Positive interaction (2-11years) (prcs03) 2 5 0.81 1 3 0.78

Ineffective parenting style (2-11 years) (prcs04) 3 7 0.70

Consistency (2-11 years)(prcs05) 2 5 0.68 1 3 0.66

Rational parenting style (2-11years) (prcs06) 2 6 0.62

PMK Depression (dpps01) 4 12 0.82 1 3 0.75



I mplications

These scales are part of a large surveyconducted every 2 years in Canada onmore than 20,000 childrenThe survey has completed 6 cycles of datacollection

Each question has been asked more than120,000 times



I mplications (Cont¶d)

The scales required 85 questionsThe revised scales require 30 questionsMore than 55,000,000 questions



Caveats

Most scales in the NLSCY are not the bestthat can be made from the available dataSome of these scales should not be usedThe NLSCY is an excellent survey,conducted by competent statisticiansSimilar results might be expected in other major surveys



Conclusions

-optifact- can help find better measures� Uni-dimensional

� Valid� Reliable

-optifact- can reduce costs

� Equivalent or better measure for same money

Optifact Summated Scales

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