- El nombre o nombres de los funcionarios que podrán imponerse de los autos

As a further illustration, we apply our algorithm to 11 personal well-being items taken from wave 6 of the European Social Survey (ESS;www.europeansocialsurvey.org), which was conducted

−0.2 0.0 0.2 −0.2 0.0 0.2 0.4 Actual Estimated Beta 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Beta: estimated vs actual

−1 0 1 −1 0 1 Actual Estimated Kappa 1 2 3 4 5 6 7

Kappa: estimated vs actual

−3 −2 −1 0 1 2 −2 0 2 Actual Estimated

Theta: estimated vs actual

Figure 4.6: A comparison of all three sets of parameter estimates with their actual values for the second penalized estimation strategy.

4.5 Applications 95 18200 18400 18600 18800 19000 19200 19400 0.0000 0.0025 0.0050 0.0075 0.0100 Penalty Out−of−sample Negativ e Log−lik elihood

Figure 4.7: Cross-validation results for the ESS data using 5 folds.

in 2012. We use only the Dutch sample of 1845 respondents. The items are summarized in Table 4.1. A rating scale with 4 categories was used, with labels ‘1 – none or almost none of the time, ‘2 – some of the time,’ ‘3 – most of the time’ and ‘4 – all or almost all of the time.’ We reversed Items 4, 6, 9 and 11 so that lower scores on these items indicate higher personal well-being, in accordance with the other items. Hence for these items the categories are effectively labelled ‘1 – all or almost all of the time,’ ‘2 – most of the time,’ ‘3 – some of the time’ and ‘4 – none or almost none of the time.’ This reversal assumes that the rating scale was interpreted symmetrically by the respondents, which we feel is a reasonable assumption for this simple scale. We apply post-stratification weights as recommended for the ESS, which adjusts for the sampling design as well as for sampling and nonresponse errors.

The penalized approach (4.26) is applied with five-fold CV to select the value of the penalty parameter. The results of this procedure are shown in Figure4.7, resulting in the optimal choice λ = 0.0025. Convergence took 77 iterations and 0.8 seconds. The estimates of the item and category parameters are given in Tables4.1and4.2respectively, and the corresponding category characteristic curves (CCCs) for the 11 items are shown in Figure4.8. As is characteristic of the RSM, the curves all have the same shape. The item parameters βj give the overall location

of the item on the latent scale θ, whereas βj + τk gives the value of the latent trait for which

the probabilities of selecting either category k − 1 or category k are equal for item j – see (4.1). Higher estimates of βj imply that θ must be comparably high before a person is likely to select

category 3 or 4 for that item, and vice versa for lower estimates of βj.

Observe that the rating categories are indeed ordered. A larger θ is associated with higher probabilities for the higher rating categories. The relatively large estimates for τ3and τ4indicate

Item 1 Item 2 Item 3 Item 4 Item 5 Item 6

Item 7 Item 8 Item 9 Item 10 Item 11

0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 −2 0 2 −2 0 2 −2 0 2 −2 0 2 −2 0 2 Theta Probability Category 1 2 3 4

Figure 4.8: The category characteristic curves (CCCs) of the 11 ESS items as fitted by the RSM. The curves show the estimated probability of choosing each category as a function of the latent trait. 0.0 0.1 0.2 0.3 0.4 −2 0 2 Theta Density

Figure 4.9: A kernel density estimate of the distribution of the estimated θ. The individual estimates are indicated on the x-axis.

4.5 Applications 97

Item Description βˆj

Please indicate how much of the time during the past week... 1 ...you felt depressed? 0.93 2 ...you felt that everything you did was an effort? 0.44 3 ...your sleep was restless? −0.17 4* ...you were happy? −0.39 5 ...you felt lonely? 1.12 6* ...you enjoyed life? −0.36

7 ...you felt sad? 0.52

8 ...you could not get going? 0.01 9* ...you had a lot of energy? −1.04 10 ...you felt anxious? −0.33 11* ...you felt calm and peaceful? −0.72

Table 4.1: The 11 ESS personal well-being items included in the Dutch sample. In our analysis, items 4, 6, 9 and 11 were reversed so that lower scores indicates higher personal well-being, in correspondence with the other items. The estimated item parameters are given in the third column. k κk τk 1 −1.37 −1.37 2 −1.50 −0.13 3 0.36 1.86 4 2.51 2.16

Table 4.2: The parameter estimates for the category parameters κ, and the corresponding τ estimates.

For a specific person i and item j, the estimated odds of choosing category 2 over category 1 is exp(θi − βj) exp(−τ2+ τ1) = 0.29 exp(θi− βj). Similarly, the estimated odds of choosing

category 3 over category 2, and of choosing category 4 over category 3, are 0.14 exp(θi− βj)

and 0.74 exp(θi− βj) respectively.

The item parameters indicate that high scores on Items 1 and 5 are associated with extremely low values of personal well-being since these items’ parameter estimates are especially high. Frequently feeling depressed and lonely therefore are strong indicators of very low levels of personal well-being. On the opposite end of the scale, Items 9 and 11 set those with extremely high personal well-being apart from others. Hence frequently feeling energetic, calm and peaceful contributes strongly to high levels of personal well-being.

The distribution of the estimated θ are summarized in Figure4.9. There are 41 persons who obtained the minimum score across all items and hence received large negative scores on the latent trait – these are the persons with the highest possible personal well-being. Theoretically, these persons would receive a θ estimate of −∞, but the penalty term in the log-likelihood has enabled a finite estimate to be found. However, this estimate will depend wholly on the penalty used. No person attained the maximum possible score.

4.6

Conclusions

In this paper we develop a novel algorithm for JML estimation of the RSM. It is shown how iterative majorization can be used to construct an iterative least-squares algorithm for maximum likelihood estimation of essentially any model that can be written in terms of the multinomial logit transform, as outlined by (De Leeuw,2011b). The method can therefore also be applied to e.g. the PCM, and the simple form of the parameter updates has the potential to enable restricted versions of these models to be fit with ease. This can be especially advantageous in the PCM, which contains many more parameters than the RSM, and we envisage investigating this in future work. Another strength of the algorithm is the ease with which missing responses can be handled.

We showed how a quadratic penalty can be included to penalize the size of the linear predictors in the model. It would also be possible to extend this to penalties on individual parameters, but together with the investigation of lasso-type penalties (Tibshirani,1996), this is left for future work. A cross-validation procedure on the out-of-sample negative log-likelihood was shown to work well for selecting the value of the penalization parameter. Furthermore, a more refined approach which penalizes relative to the scaled value of the sufficient statistics for the person parameters was found to perform even better on a simulated example. This procedure also worked well in our empirical application. We note that in the presence of a penalty term

4.6 Conclusions 99

we chose not to calculate standard errors for the parameter estimates since a penalty necessarily reduces the variance of estimates at the cost of a potential increase in the estimation bias. Hence reporting only standard errors would be likely to overstate the accuracy of estimation: an estimate of the induced bias would also be needed.

Computationally, the efficiency of the algorithm is greatly increased by the separability of the parameter updates for the three sets of parameters. This separability enables us the find the inverses of the relevant matrices explicitly, saving a substantial amount of computations. Similarly, the cross-product matrices can be shown to perform simple summations over three-way arrays, which negates the need for matrix products in the updates completely. We feel that JML estimation combined with regularization is an attractive alternative method to CML and MML estimation.

CHAPTER

5

Competing for the Same Value Segments:

Insight into the Volatile Dutch Political

Landscape

5.1

Introduction

Recent years have seen substantial changes to political landscapes in many countries (Van der Meer et al.,2015), including the Netherlands. Major political parties such as the CDA (Christian Democrats) have lost ground to new parties, most notably the LPF (Pim Fortuyn List) and the populist PVV (Party for Freedom), which launched in 2002 and 2006 respectively. Concurrently, the proportion of the electorate choosing to abstain from voting is on the rise, possibly due to a growing separation between voters and political parties as the latter fail to align their political agendas with voters’ values.

Human values are deeply ingrained in a people’s psyche and direct their behaviour, especially abstract behaviour such as voting in elections (Schwartz et al.,2010;Caprara et al.,2006;Barnea and Schwartz,1998). Political parties appeal to political values such as safety and security, freedom of speech and concern for one’s fellow man that closely resemble human values such as security, self-direction and universalism (Schwartz et al.,2013). It is therefore to be expected that people will be more likely to vote for the political party that best reflects their own values. Previous research has focused on relationships between human values and choosing whether to vote or abstain (Caprara et al.,2012), the left-right dimension in politics (Thorisdottir et al.,

2007), and value preferences of people voting for specific political parties (Barnea and Schwartz,

1998).

This study reports on an empirical investigation into the relationship between human values and political preference in the Netherlands. All political parties and values are considered simultaneously, using data collected for five waves of the European Social Survey. Schwartz

(1992)’s Human Values Scale, comprising of 21 survey items measured on 6-pointLikert(1932) scales, is used to assess individuals’ values. Self-reported voting behaviour in national elections is also available. These data span the years 2002 until 2010, giving insight into concurrent changes in voting behaviour and human values. Whilst until now research has focused on values separately (Schwartz et al.,2010;Barnea and Schwartz,1998), we interpret combinations of values that together influence voting behaviour. Such combinations of values are termed ‘value segments’ hereafter.

The established method of measuring human values is by using rating scales. This requires correcting for response styles (Schwartz,2007), since comparing responses between different survey participants should account for the heterogeneous use of rating scales pervasive in such studies (e.g.Van Vaerenbergh and Thomas,2013;Baumgartner and Steenkamp,2001). Only after disentangling these response styles from substantive content can valid comparisons be made. However, few studies correct for response styles as it is difficult and content-related information might be removed in the process (Schoonees et al.,2015b). Recently, more advanced alternatives to the commonly used response style indices advocated byBaumgartner and Steenkamp(2001) have been developed. Specifically, we use the latent-class bilinear multinomial logit (LC-BML) model ofVan Rosmalen et al.(2010), which allows us to estimate value segments while at the same time correcting for differences in response style. This correction results in more valid value segments.

The questions we pose in this study are as follows: How many content-based value segments are there in the Dutch population and how are these value segments related to voting behaviour? How stable is the relationship between the value segments and the political parties over time? What effect do individual differences in response style have on content-based value segments? We start by giving an overview of political dimensions and cultural value theory applied to Dutch politics, a short summary of important recent events affecting voting, and an overview of our research propositions. Then we will further describe the LC-BML model and present our results. We end with a discussion and show the relevance of our method to study political change in other multi-party political systems.