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Erschienen in:
Building Models for Markets Kapitel lesen Erstes Kapitel lesen

2015 | OriginalPaper | Buchkapitel

5. Validation and Testing

verfasst von : Peter S. H. Leeflang, Jaap E. Wieringa, Tammo H. A. Bijmolt, Koen H. Pauwels

Erschienen in: Modeling Markets

Verlag: Springer New York

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Abstract

Two critical steps in the model building process are model specification and model estimation. In this chapter we turn to the next stage in model building: validation (also verification or evaluation).

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Vorheriges Kapitel Estimation and Testing
Nächstes Kapitel Re-estimation: Introduction to More Advanced Estimation Methods
Fußnoten
1
Ramsey (1969, 1974) .
 
2
See also Judge et al. (1985, p. 453); Wooldridge (2012, p. 269).
 
3
Tabulated values of d L , d U for different significance levels can be found in most textbooks on econometrics.
 
4
For other stochastic processes such as moving average processes and combined autoregressive moving average processes, see, e.g., Judge et al. (1985, Chapter 8).
 
5
The residuals are standardized by dividing the observed values by the standard deviation of the residuals (the average of the residuals equals zero under usual conditions).
 
6
See Shapiro and Wilk (1965).
 
7
See Bera and Jarque (1981, 1982) ; Stewart (1991, p. 162).
 
8
For a discussion of theoretical arguments and empirical generalizations, see Kaul and Wittink (1995).
 
9
See Farrar and Glauber (1967); Kumar (1975) or Friedman (1982).
 
10
Currently, the spectral decomposition of X′X is advocated for the quantification of multicollinearity, based on one or more characteristic roots. In this respect researchers quite often use the condition numbers of X′X, that is the square root of the ratio of the largest to smallest eigenvalue of X′X; see Cameron and Trivedi (2009, pp. 350–351).
 
11
See also Rao et al. (1988).
 
12
See, for example, Massy (1965) and Sharma (1996, Chapter 4).
 
13
Available from Selig and Preacher at http://​www.​quantpsy.​org/​medmc/​medmc.​htm.
 
14
Chow (1960); Fisher (1970).
 
15
This section is based on Bult et al. (1997). For an extensive discussion of causality tests see the special issues of the Journal of Econometrics, vol 39 (1–2). For overviews of causality tests applied in marketing see Hanssens et al. (2001, p. 314). We note that we use the concept of “causality” that can be tested with statistical methods. This concept is not based on cause and effect in a strict philosophical sense (see Judge et al. 1985, p. 667).
 
16
Multivariate causality tests, such as the VARMA-model (Judge et al. 1985, p. 667), can be used to detect causality or to determine the direction of causality in a fully specified model. For an application of the VARMA-model see Boudjellaba et al. (1992).
 
17
Analytical arguments for these tests can be found in for example Chow (1983).
 
18
This test has been used in a marketing context by, for example, Hanssens (1980a,b) and Leeflang and Wittink (1992).
 
19
See for example Alba (2011).
 
20
The criticism will be muted if a coefficient with a sign opposite to expectations is not statistically significant. If the sign is “wrong” and the coefficient is significantly different from zero, we would suspect model misspecification.
 
21
Compare (Rust et al. 1995a, 1955b).
 
22
See, for example, Foekens et al. (1999) and the discussion in Sect. 5.4.1.
 
23
Other reformulations are found in Akaike (1981).
 
24
See also Sect. 5.2.4.
 
25
See Wittink (1988, p. 47).
 
26
Note that the sum of the residuals is equal to zero by construction. Hence, any test on the average of the residuals is not very informative.
 
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Metadaten
Titel
Validation and Testing
verfasst von
Peter S. H. Leeflang
Jaap E. Wieringa
Tammo H. A. Bijmolt
Koen H. Pauwels
Copyright-Jahr
2015
Verlag
Springer New York
Buch
Modeling Markets

Print ISBN: 978-1-4939-2085-3

Electronic ISBN: 978-1-4939-2086-0

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-1-4939-2086-0_5