Comparing Reflective and Formative Measurement Models on the Same Indicators

1
Comparing Reflective and Formative Measurement
Models on the Same Indicators

• George R. Franke, University of Alabama
• Nick Lee, Aston University

2
Formative Principles

• The indicators cause the construct
• Indicators need not be correlated
• Omitted indicators omit part of the construct
• Error term is structural (effect of omitted
  causes), not measurement
• The construct depends on its outcomes, not just
  its indicators

F/R
3
Reflective Principles

• The construct causes the indicators
• Indicators should be internally consistent
• Equally-reliable indicators are substitutable
• Error terms are measurement error
• Different antecedents and outcomes of the
  construct have limited effects on the indicators

R
R
4
Measurement (mis?)specification

• One common view only one model is right or
  wrong for each construct
• Wrong model causes major problems
• Diamantopoulos Siguaw (2006) Type I and
  Type II errors from misspecification
• Various estimates of misspecification rates
• 29 in marketing
• 31 in information systems
• 47 in leadership
• 69 in strategy

5
Measurement (mis?)specification

• Purported consequences
• misspecification of even one formatively
  measured construct within a typical structural
  equation model can have very serious consequences
  for the theoretical conclusions drawn from that
  model (Jarvis, MacKenzie Podsakoff 2003, p.
  212)
• misspecification can inflate unstandardized
  structural parameter estimates by as much as 400
  or deflate them by as much as 80 (MacKenzie,
  Podsakoff Jarvis 2005, p. 728)

6
Alternative Views

• A given set of indicators may (possibly) be
  modeled equally well as formative or reflective
• A given construct may (possibly) be measured
  formatively or reflectively
• Model fit and relationships between constructs
  are not necessarily fundamentally affected by the
  modeling approach

7
Formative model, R2 .30, n400
t 1.98
t 7.74
8
Reflective specification, R2 .36
t 15.03
t 8.16
t 7.74
9
Hybrid specification, R2 .30 (reduced R2
.25 indirect effect of KSI on ETA, t 7.90)
t 1.98
t 14.92
X1
.14
.71
X2
Y1
.14
.71
.71
.14
.71
KSI
ETA
X3
.71
.14
.71
Y2
.14
t 7.74
X4
.71
X5
Chi-Square0.00, df9, P-value1.00000,
RMSEA0.000
10
Comparison
11
Empirical comparison, MPJ 2005
Case A Exogenous and Endogenous Formative
Correlations 0.5




















1
1
1
1
1
1
1
1
1
1
V1
V2
V4
V5
V3
V8
V9
V11
V12
V10
1
1
1
1
1
1
1
1
1
1
0.3
Construct A
Construct B
1
1
D1
1
1
1
1
D2
0.50
0.50
V6
V7
V13
V14
1
1
1
1
E7
E13
E14
E6
0.32
0.32
0.32
0.32
12
Empirical comparison, MPJ 2005
Case A Standardized values
Correlations 0.5




















1
1
1
1
1
1
1
1
1
1
V1
V2
V4
V5
V3
V8
V9
V11
V12
V10
.25
.25
.25
.25
.25
.24
.24
.24
.24
.24
.29
Construct A
Construct B
1
1
D1
.99
.99
.99
.99
D2
.03
.03
V6
V7
V13
V14
1
1
1
1
E7
E13
E14
E6
.02
.02
.02
.02
13
Empirical comparison, MPJ 2005
Case B Exogenous Reflective
E1
E2
E3
E4
E5
1
1
1
1
1
1
1
1
1
1
V1
V2
V4
V5
V3
V8
V9
V11
V12
V10
1
1
?
Construct A
Construct B
1
1
D1
D2
V6
V7
V13
V14
1
1
1
1
E7
E13
E14
E6
14
Empirical comparison, MPJ 2005
Case C Endogenous Reflective
E8
E9
E10
E11
E12
1
1
1
1
1
1
1
1
1
1
V1
V2
V4
V5
V3
V8
V9
V11
V12
V10
1
1
?
Construct A
Construct B
1
1
D1
D2
V6
V7
V13
V14
1
1
1
1
E7
E13
E14
E6
15
Empirical comparison, MPJ 2005
Case D Exogenous and Endogenous Reflective
E1
E2
E3
E4
E5
E8
E9
E10
E11
E12
1
1
1
1
1
1
1
1
1
1
V1
V2
V4
V5
V3
V8
V9
V11
V12
V10
1
1
1
?
Construct A
Construct B
1
1
D1
D2
V6
V7
V13
V14
1
1
1
1
E7
E13
E14
E6
16
Population data, n500
v1
v2
v4
v5
v3
v8
v9
v11
v12
v10



1.0 (t13.78)
1.0 (tna)



1.0 (t13.64)
1.0 (tna)
.30 (t13.65)
A
B
standardized .29
1.0 (t21.25)

1.0 (t21.03)

v6
v7
v13
v14
Chi-sq 0, df 66, RMSEA 0
17
Population data, another scaling
v1
v2
v4
v5
v3
v8
v9
v11
v12
v10
.30 (t17.82)




1.0 (t21.03)




1.0 (tna)
A
B
standardized .29
3.33 (t31.35)
1.0 (tna)
1.0 (t113.02)
3.33 (t31.35)
v6
v7
v13
v14
Chi-sq 0, df 66, RMSEA 0
18
Population data, final scaling
v1
v2
v4
v5
v3
v8
v9
v11
v12
v10



1.0 (t21.25)



1.0 (t21.03)


.30 (t31.35)
A
B
standardized .29
1.0 (t108.26)
1.0 (tna)
1.0 (tna)
1.0 (t113.02)
v6
v7
v13
v14
Chi-sq 0, df 66, RMSEA 0
19
Comparison
20
Conclusions from Analysis

• It is not necessarily a case of right/wrong, but
  either/or
• Do you focus on individual (formative) or common
  (reflective) effects?
• Evidence for one model does not necessarily
  preclude the other
• Choice of model may have minimal impact on
  estimated structural relationships

21
Theoretical Implications

• Formative and reflective models imply different
  upfront measure development activities
• These may result in different sets of measurement
  indicators
• formative variety of moderately-correlated
  indicators to maximize variance explained while
  limiting collinearity
• reflective fewer highly-correlated indicators to
  maximize reliability and interpretability

22
Practical Implications

• It is becoming more common to recommend formative
  treatment of reflective indicators
• Our results suggest that for a given set of
  indicators, choice of model may not be of major
  importance to structural relationships

23
Conclusion

• Our results support calls for the field as a
  whole to think more carefully about measurement
  model relationships and do a better job of making
  sure that the measurement models used match that
  conceptualization (Jarvis, MacKenzie and
  Podsakoff 2003, p. 216)