Standardising the reproduction of Schwartz’s two-dimensional value space using multi-dimensional scaling and goodness-of-fit test procedures

Abstract

Numerous empirical studies based on Schwartz’s famous Theory of Basic Values also use his Portrait Values Questionnaire to collect data. Many of these follow Schwartz by using multi-dimensional scaling (MDS) and goodness-of-fit (GoF) tests to ascertain the extent to which their empirical results reproduce his two-dimensional model and visually represent the results. A small number report their analytical procedures in some detail, however, most mention MDS and accompanying measures of GoF without providing sufficient detail. This omission creates problems for researchers wanting to undertake comparative work across these values studies that use MDS together with GoF tests. Bilsky et al. (J Cross Cult Psychol 42(5):759–776, 2011) advocate careful description of MDS methods, which allows easy reproduction by others. This is an important step towards consistency and transparency that promote rigorous scientific practice. However, these procedural steps could be more detailed, standardised and even automated. In this paper we argue for the standardisation of Schwartz et al.’s MDS and GoF procedures. To this end, we methodically describe and introduce our computer programme (S2-D) to automate almost all the steps. We also introduce two new ways of measuring the GoF.

Appendices

Appendix 1: Schwartz’s PVQ items and values

See Table 4.

Table 4 PVQ items and values (female version) (Schwartz 2009)

Appendix 2: IBM-SPSS syntax

2.1 Starting configuration for Schwartz’s value space

The syntax for the starting configuration is as follows:

2.2 IBM-SPSS syntax for mean centering

The syntax for mean centering is as follows:

2.3 IBM-SPSS syntax for MDS/SSA

The syntax for the MDS/SSA is as follows:

Note:

• 1.) In the above syntax command

we use “ORDINAL” because it guarantees that Kruskal’s (1964) ordinal MDS is applied, and we use “KEEPTIES” to specify that the ties (i.e. equal correlations) are taken into account in the computation (see, for example, Borg et al. 2013).

• 2.) Importantly, copy the above syntax exactly as it is and do not change anything.

Appendix 3: Expected number of border crossings

We make the assumption that a PVQ item is randomly located in Schwartz’s value scale. Accordingly, the following events (or outcomes) are possible:

• The PVQ item is placed in the correct sector. No border has to be crossed.

• The PVQ item is placed in the next sector to the right. One border has to be crossed.

• The PVQ item is placed in the second sector to the right. Two borders have to be crossed.

If we ignore the border between Conformity and Tradition for a moment, nine events are possible. Each event has the probability of 1/9. If a PVQ item is misplaced, we can move the item point clockwise or anti-clockwise in order for it be located in the right sector. Table 5 shows the shortest path, which results in an expected value of $E(no.borders/item) = 2.22$.

Table 5 Possible location of a randomly distributed item in Schwartz’s value space

Because one PVQ item is always correct, we have to compute the expected value for 20 items and not 21 items. The value is:

$$E(no.boarders) = E(no.borders/item) \cdot no.items = E(no.borders/item) \cdot 20 = 44.4$$

Until now, we have ignored the awkward additional border in Schwartz’s two-dimensional value space between Tradition and Conformity There are four different possible outcomes if the items are located randomly in these two sectors (Table 6).

Table 6 Possible location of a randomly distributed items in the tradition and conformity sectors in Schwartz’s value space

The expected number is 1. Adding this number, the expected value becomes $E(no.borders) = 44.4 + 1 = 45.4$.