marketing

1
An extended paradigm for measurement analysis
applicable to panel data Hans Baumgartner Penn
State University Jan-Benedict E.M. Steenkamp UNC
Chapel Hill
2
The conventional measurement model

• The widespread adoption of structural equation
  modeling has greatly increased researchers
  concern with the validity and reliability of
  construct measurement

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?1
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Shortcomings of the conventional measurement
model

• temporary and stable components of a construct
  are not separated
• measure specificity and other sources of
  systematic but non-construct-related variation in
  yij are confounded with random measurement error
• the means of observed and latent variables are
  not considered explicitly

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Stable and transitory components of a construct

• It is one thing to be irascible, quite another
  thing to be angry, just as an anxious temper is
  different from feeling anxiety. Not all men who
  are sometimes anxious are of an anxious
  temperament, nor are those who have an anxious
  temperament always feeling anxious. In the same
  way there is a difference between intoxication
  and habitual drunkenness
• Cicero (45 B.C.)

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The concepts of trait and state

• temporal stability (whether the personal
  characteristic is enduring or temporary) as the
  central aspect of the distinction (Chaplin, John,
  and Goldberg 1988)
• well-known in the personality literature
• difference between enduring and situational
  involvement as the best marketing example

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How often is stability assessed in marketing
scales?

• some scales are explicitly meant to assess stable
  individual differences (e.g., chronic behaviors,
  enduring beliefs, general traits)
• other scales are specifically designed to measure
  states (e.g., moods and emotions)
• 23 of the 192 scale development efforts reviewed
  in Bearden and Netemeyer (1999) report a
  test-retest correlation

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Systematic and random sources of measurement error

• usually, the observed variance is partitioned
  into two components, substantive variance and
  (random) error variance
• failure to distinguish between different forms of
  measurement error leads to the following
  problems
• the causes of measurement error seem mysterious
• the relative importance of different forms of
  measurement error remains unknown
• systematic patterns of covariation among the
  observed variables that differ from those caused
  by substantive factors are ignored

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Effect of systematic error on comparisons of
means(Steenkamp and Baumgartner 1998)

• representative samples of respondents from
  Denmark, France, Netherlands, and Portugal
  indicated their attitude toward advertising on 5
  five-point Likert scales
• the country means based on raw and latent scores,
  using Denmark as the baseline (raw mean of 2.47),
  were as follows
• raw means latent means
• DE 0 0
• FR .028 .059
• PO -.058 -.139
• NL -.078 -.501

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Effect of systematic error on correlations
between substantive scales (Baumgartner and
Steenkamp 2001)

• HCO QCO ECO CET
• (22) (14) (12) (16)
• HCO --
• QCO .40 (.20) --
• ECO .33 (.15) .31 (.13) --
• CET .28 (.02) .19 (.00) .15 (.01) --

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Comparison of construct means across groups and
over time

• comparisons of means are sometimes an explicit
  component of the construct validation process
• most scales are eventually used to compare
  construct means across groups or over time
• these comparisons are only meaningful if certain
  conditions of measurement invariance are
  satisfied

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A multi-construct, multi-item, multi-occasion
measurement model

• distinguishes temporary and stable components of
  variance in constructs corresponding to their
  trait and state aspects
• separates systematic sources of non-construct
  variance (e.g., measure-specific variance) from
  random measurement error
• takes into account the means of the observed
  scores

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A multi-construct, multi-item, multi-occasion
measurement model
yijt ? a persons score on the ith item of
construct j at time t ?jt ? an occasion-specific
measure of construct j at time t ?ijt ? a
composite of all error terms ?ijt ? factor
loading ?ijt ? measurement intercept
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Modeling states and traits
?jt ? an occasion-specific measure of construct
j at time t ?Sj ? stable (trait) component of
construct j (S for stable) ?Tjt ? transitory
(state) component of construct j (T for
transitory) ?jt ? second-order factor loading
?jt ? equation intercept
16
(No Transcript)
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Modeling states and traits (contd)

• the total variation in ?jt can be decomposed into
  two orthogonal components
• trait variation (perfectly stable over time)
• state variation (perfectly unstable)
• the proportion of trait variation should be above
  .5 for a trait measure and below .5 for a state
  measure
• the correlation between ?jt and ?jt' depends on
  the proportion of trait and state variation at t
  and t'

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Modeling random and systematic sources of
measurement error
?ijt ? random measurement error (cell 1) ?ijSIE
? stable item-specific error (cell 2) ?tTSE ?
transient item-subset error (cell 3) ?SSE ?
stable item-subset error (cell 4) ?tTWE ?
transient scale-wide error (cell 5) ?SWE ?
stable scale-wide error (cell 6)
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Stable (item-)subset error
Transient (item-)subset error
Stable item-specific error
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Variance decomposition

• Substantive variance
• Trait variance
• State variance
• Non-substantive variance
• Random error variance
• Stable item-specific error variance
• Transitory item-subset error variance
• Stable item-subset error variance
• Transitory scale-wide error variance
• Stable scale-wide error variance

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Modeling the means of the constructs

• to identify the model
• the measurement intercepts ?ijt associated with
  the marker items for the occasion-specific
  factors ?jt are set to zero
• the equation intercepts ?jt associated with the
  marker factors for the trait factors ?Sj are set
  to zero
• one can test for the equality of the means of the
  ?jt or ?jS across groups or of the means of the
  ?jt over time
• (partial) metric and scalar invariance is
  necessary for comparisons of means to be
  meaningful (Steenkamp and Baumgartner 1998)

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Empirical illustrationBrand loyalty and deal
proneness

• data from 1991 Dutch consumers for 2000, 2002,
  and 2003
• five-item brand loyalty scale
• Once I get used to a brand, I hate to switch.
• When another brand is on sale, I generally
  purchase it rather than my usual brand.
• I feel really committed to the brand I buy.
• If my preferred brand were not available at the
  store, it would make little difference to me if I
  had to choose another brand.
• Even though certain products are available in a
  number of different brands, I always tend to buy
  the same brands.

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Empirical illustrationBrand loyalty and deal
proneness

• four-item deal proneness scale
• I enjoy buying products that are on offer.
• In general, I do not respond to promotional
  offers.
• Buying brands on offer makes me happy.
• I love special promotional offers.
• all items rated on five-point Likert scales with
  endpoints of completely disagree and
  completely agree

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Model comparisons
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Model comparisons
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Are brand loyalty and deal proneness traits or
states?

• t1 t2 t3
• Brand loyalty
• Trait variation .78 .92 .87
• State variation .22 .08 .13
• Deal proneness
• Trait variation .67 .84 .80
• State variation .33 .16 .20

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Variance decomposition for BL items

• Trait State Stable Stable Transient Stable
  item Random
• scale-wide item-subset item-subset specific
• BL11 .39 .11 .04 .05 .02 .07 .32
• BL21 .29 .08 .04 .02 .00 .09 .49
• BL31 .32 .09 .04 .06 .02 .10 .37
• BL41 .25 .07 .05 .02 .00 .17 .45
• BL51 .31 .09 .05 .06 .02 .08 .39
• BL13 .43 .04 .05 .06 .02 .06 .35
• BL23 .32 .03 .05 .02 .00 .08 .50
• BL33 .37 .03 .05 .06 .02 .16 .31
• BL43 .26 .02 .05 .02 .00 .17 .47
• BL53 .30 .03 .06 .07 .02 .15 .37
• BL14 .45 .07 .05 .06 .02 .06 .29
• BL24 .33 .05 .05 .02 .00 .15 .41
• BL34 .35 .05 .04 .06 .02 .18 .30
• BL44 .26 .04 .05 .02 .00 .18 .45
• BL54 .32 .05 .06 .07 .02 .12 .36

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Scale-level variance decompositionfor brand
loyalty

• Substantive variance 39
• Trait variance 33
• State variance 6
• Non-substantive variance 61
• Stable scale-wide error variance 5
• Stable item-subset error variance 4
• Transient item-subset error variance 1
• Stable item-specific error variance 12
• Random error variance 39

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Average variance extracted and composite
reliability by time periodBrand loyalty

• t1 t2 t3
• Average trait variance extracted .31 .34 .34
• Average state variance extracted .09 .03 .05
• Average substantive variance .40 .37 .39
• extracted
• Trait reliability .56 .63 .61
• State reliability .16 .06 .09
• Substantive reliability .72 .68 .70

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Variance decompositions for DP items

• Trait State Stable Stable Transient Stable
  item Random
• scale-wide item-subset item-subset specific
• DP11 .22 .11 .07 .09 .03 .02 .47
• DP21 .22 .11 .05 .02 .00 .06 .53
• DP31 .08 .04 .04 .05 .02 .25 .52
• DP41 .31 .15 .05 .06 .02 .03 .37
• DP13 .27 .05 .07 .09 .03 .07 .42
• DP23 .21 .04 .06 .02 .00 .09 .59
• DP33 .06 .01 .05 .06 .02 .30 .50
• DP43 .35 .07 .05 .06 .02 .13 .31
• DP14 .23 .06 .08 .10 .03 .11 .39
• DP24 .16 .04 .06 .02 .00 .10 .62
• DP34 .06 .02 .05 .06 .02 .29 .51
• DP44 .34 .08 .05 .07 .02 .05 .40

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Scale-level variance decompositionfor deal
proneness

• Substantive variance 28
• Trait variance 21
• State variance 7
• Non-substantive variance 72
• Stable scale-wide error variance 6
• Stable item-subset error variance 6
• Transient item-subset error variance 2
• Stable item-specific error variance 13
• Random error variance 47

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Average variance extracted and composite
reliability by time periodDeal proneness

• t1 t2 t3
• Average trait variance extracted .21 .22 .20
• Average state variance extracted .10 .04 .05
• Average substantive variance .31 .27 .25
• extracted
• Trait reliability .36 .40 .37
• State reliability .18 .08 .09
• Substantive reliability .54 .48 .46

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Effect of systematic error on correlation
between BL and DP

• r(BL1, DP1) r(BL2, DP2) r(BL3, DP3)
• Raw -.22 -.16 -.16
• Corrected for -.29 -.22 -.23
• random error .81, .71 .80, .68 .81, .66
• Corrected for -.36 -.36 -.37
• nonsubstantive error .72, .54 .68,
  48 .70, .46
• Corrected for -.58 -.63 -.65
• all errors

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How does this discrepancy arise?

• observed correlation consists of true observed
  correlation (which is negative) and systematic
  error correlations (which are positive)
• when -.36 is disattenuated using the substantive
  reliability estimates, we get -.58, which is the
  true correlation
• however, if -.22 is disattenuated, we dont get
  the true correlation

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Comparison of means

• both scales exhibit full metric invariance over
  the three-year time period
• two measurement intercepts are variant, but
  otherwise scalar invariance is satisfied
• brand loyalty and deal proneness have changed
  little over time
• t1 t2 t3
• BL 3.16 3.20 3.16
• 3.31 3.31 3.34
• DP 3.70 3.68 3.71
• 3.07 3.11 3.08

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Conclusions

• The proposed model
• enables a differentiation between the state and
  trait components of a construct (an item should
  contain a high proportion of the appropriate kind
  of substantive variance)
• accounts for a variety of sources of measurement
  error (management of measurement error
  necessitates an understanding of its sources)
• properly considers item and construct means in
  measurement analysis (measurement invariance has
  to be assessed more explicitly, and it should be
  a criterion for choosing appropriate items)