International Choice Modelling Conference, International Choice Modelling Conference 2015

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EXTENDING ICLV MODELS BY ACCOUNTING FOR ENDOGENEITY AND COUNTERFACTUAL THINKING
George Chryssochoidis

Last modified: 18 May 2015

Abstract


1.Introduction

 

The aim of the present endeavor is to advance integrated discrete choice and latent variable (ICVL) models by correcting and accounting for endogeneity and counterfactual thinkiung regarding the causal links in the factorial (latent) structures.

 

The reason is as follows: Research is at cross-roads. Lack of considering confounding or counterfactual thinking are now seen as having substantially biased past research. ‘Confounding’ has been defined primarily as non-modelling model-relevant variables (‘confounders’) (VanderWeele and Shpitser, 2013) resulting to inaccurate estimates (Antonakis et al., 2010). Moreover, causal quantities (unlike associational reasoning mostly practiced under a SEM framework) (Holland, 1988) involve a notion of how the world would have been had should an element been different (Pearl, 2012). Take for instance a mediation model where the effect of an independent variable affects the choice through another independent variable (the mediator) [thus X-->M--> Choice Dependent]. The definition of direct and indirect effects involves indeed quantities that are not all observable: Y(x): the potential values of Y that would have occurred had X been set, possibly counter to fact, to the value x; M(x): the potential values of M that would have occurred had X been set, possibly counter to fact, to the value x; Similarly for Y(x, m) and Y(x, M(x*)).

Thankfully, work–especially in economics and epidemiology- proposes methods to deal with confounding and also causal (counterfactuals) effects estimation and have produced an armoury of approaches. These include for instance: a) Instrumental variables-based (e.g., Garen, 1984); b) Strata based  (Emsley et al., 2010); c) Propensity score matching (Guo and Frazer, 2010); d) VanderWeele’s 4-way effect decomposition (VanderWeele, 2014); e) Paramed (Emsley and Liu, 2013); f) Imai et al. (2010a; b; 2011) approach; g) Muthen and Asparouhov (in-press) approach; h) Latent IV (Ebbes et al., 2009) approach. Yet, no comparative study has ever considered these in the discrete choice literature, identify the premises as well as the (dis)similarities of the outcomes produced by these alternative suggested solutions. 

 

This paper will extend the ICVL literature correcting theory and model specification/ estimation with respect to counfounding and counterfactuals. To do so, I take a standard ICVL model and data from 2 existing ICVL experiments, demonstrate the logic behind the proposed correction approaches and also the differences in estimates.  The 1st dataset comes from a UK Energy Research Centre project focusing on home renovation decisions (VERD) (http://www.ukerc.ac.uk/support/RF3LEnergyEfficientHomeRenovations) and the 2nd dataset comes from the most important EU FP7 funded study (FLABEL) (http://www.flabel.org/en/) for food nutritional labelling.

 

2.Background

 

2.1. ICVL Models: Walker (2001) had already mentioned (p. 24) that at the core of the DCE model which is based around a standard multinomial logit model, extensions are added to relax simplifying assumptions and enrich the capabilities of the basic model, and that among these extensions are:

  • First, a factor analytic (probit-like) disturbances in order to provide a flexible covariance structure, thereby relaxing the IIA condition and enabling estimation of unobserved heterogeneity through, for example, random parameters.

  • Second, the incorporation of latent variables in order to provide a richer explanation of behavior by explicitly representing the formation and effects of latent constructs such as attitudes and perceptions.

     

    Work subsequently picked up by several researchers and references in the area include –among others, Morikawa and Sasaki (1998), Ashok et al. (2002), Ben-Akiva et al. (1999; 2002; 2002), Bierlaire (2003) and the latest version of Biogeme, Walker and Li (2007), and Bolduc et al. (2005), but also Zeid (2009), Temme et al. (2008), Hess and Stathopoulos (2010) and Danthurebandara et al. (2013). Ashok et al. (2002) showed how to do so in a simultaneous manner although their approach was constrained by the number of latent factors to include in the ICLV model. Temme et al. (2008) extended the classical travel mode choice model to incorporate individuals' attitudes and values and showed how to include a larger number of latent variables in ICLV models. Rungie et al. (2011) proposed and described a comprehensive theoretical framework that integrates choice models and structural equation models, referred to as “structural choice modelling, Across almost all efforts, the ICLV model was based on the conditional logit model and the market heterogeneity was modelled by incorporating individuals’ specific latent factors while at the same time a parallel effort has often been used to model the market heterogeneity. Nonetheless, none has considered the effects of either confounding or counterfactual thinking. This is an important area that requires further investigation.

 

2.2. Confounding assumptions in causal processes:  ‘Confounding’ may be associated with variables non-nominated in a focus statistical model (‘confounders’) (VanderWeele and Shpitser, 2013)  or methodology aspects. In this respect a confounder may be defined as a pre-exposure variable (‘C’) associated with X and associated with the Y conditional on an W, possibly conditional also on other covariates (Miettinen, 1974). Heckman’s (1979) attributed this to selection-bias. If so, it is anticipated that unmodelled correlations exist, false positive (Type I) errors are produced and this threatens internal validity and causal inference. Antonakis et al. (2010) correctly identified 7 separate relevant aspects, namely: a) omitted variables; b) omitted selection; c) simultaneity; d) measurement error; e) common-method variance; f) inconsistent inference; and g) model mispecification. Extensions have also included what is defined as ‘intermediate confounding’ which is the situation where confounders themselves are affected by the variable X a situation common in epidemiology settings (Stabola et al., in-press).

 

2.3. Counterfactual thinking practiced as SEM (or ICVL): SEM is a cornerstone regarding specifying and identifying links. Yet, correlation does not prove causation (Wilkinson and Task Force, 1999 in Bollen and Pearl, 2013). Pearl making a strong comment argues that ‘the entire literature in econometric research... has been misguided, for researchers have been chasing parameters that have no causal interpretation Pearl, 2012: 68). To disperse the confusion about this it has been clearely stated that SEM does not aim to establish causal relations from associations alone (Bollen and Pearl, 2013). This is best demonstrated when explaining causal direct and indirect effects.  In the case of a traditional mediational model its statistical form is:

                                                                       (1)         and       

                                                                                  (2)

and therefore (Hayes, 2013):

  • the direct effect of X upon Y = c1'

  • the indirect effect of X upon Y through M = α1*β1

  • the total effect of X upon Y= direct effect + indirect effect                                          

 

In contrast to the traditional definition, the newer definitions based upon counterfactual thinking include (Robins and Greenland, 1992; Pearl, 2001; 2009):

  • controlled direct effect: the effect of X on Y that would be observed if the mediator were controloled uniformly at a fixed value (usually 0). In other words E { Y(XValue1, 0) – Y(XValue2, 0)}.

  • natural direct effect: given that it may not be realisitic to think of forcing the mediator to be the same for all study subjects allow for a natural variation in the level of the mediator between study subjects. An indivifual study subject’s ‘natural level’ of the mediator is taken to be the counterfactual value M(0) it would have taken if the X were in a randomised experiment 0. In other words E { Y(XValue1, M(0)) – Y(XValue2, M(0))}.

  • natural indirect effect is subsequently provided by total effect – natural direct effect.

 

2.4 Solutions: Approaches to correct for endogeneity and using counterfactual thinking. Several approaches have been developed and these included:

 

  1. Confounding correction with principal strata membership (Emsley et al., 2010) approach

  2. Confounding correction using Instrumental Variables–2SLS/Garen’s (1984) approach.

  3. Confounding Correction Using a Causal-thinking Propensity Score (PS)/SMM (Guo and Frazer, 2010) approach.

  4. Confounding Correction using the Latent IV (Ebbes et al., 2009) approach

  5. Counterfactual –Based Correction using VanderWeele’s (2014) 4-way decomposition

  6. Counterfactual –Based Correction using the Paramed (Emsley and Liu, 2013) approach

  7. Counterfactual –Based Correction using the Imai et al. (2010a; b; 2011) approach

  8. Counterfactual –Based Correction using the Muthen and Asparouhov (2014) approach

     

3. Paper Content and Direction

 

The merging of thinking between ICVL and counfounding correction/ counterfactuals’ thing has not happened so far and no work exists thereof. In the paper, I will explain each proposed approach for the matter, I will delineate the pros and cons of each one of these approachs for the purpose of ICVL models. Subsequently, I will implement these approaches within the overall context of a traditional ICVL experiment using as examples both 2 datasets and demonstrate the differences in estimates but also the fundamental differences in theoretical outcomes and conceptualisations.

 

References

 

Abou Zeid, M. (2009) Measuring and modeling travel and activity well-being, Ph.D. Thesis, Massachusetts Institute of Technology.

Antonakis J., Bendahan S., Jacquart P. & Lalive R. (2010). On making causal claims: A review and recommendations. The Leadership Quarterly, 21(6), 1086-1120.

Ashok, K., W.R. Dillon, and S. Yuan, 2002. Extending Discrete Choice Models to Incorporate Attitudinal and Other Latent Variables. Journal of Marketing Research 39(1) 31-46.

Ben-Akiva, M., J. Walker, A. Bernardino, D. Gopinath, T. Morikawa, and A. Polydoropoulou, 2002. Integration of Choice and Latent Variable Models, in (H. Mahmassani, Ed.) In Perpetual Motion: Travel Behaviour Researc


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