International Location Index for the Medium-Sized Companies
The choice of indicators is based on the theoretical framework described in paragraph 3.1. Accordingly, the selection criterion was the theoretical relevance of a particular item, which was applied consistently for all indicators. Nonetheless, the accuracy with which the items of the index or sub-indices measure the relevant construct needs to be tested. This was carried out by means of a Cronbach's alpha analysis.  Cronbach's alpha is the most commonly used measure to test the internal consistency of a scale that is composed of several variables. Due to the large variances of the individual indicators, they were first standardised to a standard deviation of one and a mean value of zero.
The alpha coefficient for the 20 items that make up the index is 0.9192. This indicates a relatively high internal consistency. Cronbach's alpha for the eight items of the "economic conditions" dimension (one of three dimensions of the BDO International Business Compass) is 0.7412. The "per capita income" has the strongest correlation with the other items of this dimension. The measure for the six items of the "political conditions" dimension is 0.9260. In this case, the "regulatory quality" indicator has the strongest correlation with the other items. Cronbach's alpha for the "social conditions" dimension achieves a value of 0.6828. Hence, the value of the reliability coefficient is just sufficient. In this dimension, "education" has the strongest correlation with the other items of the sub-index.
The sub-indices "sales market" and "production site" both achieve values above the threshold, which indicates a relatively high internal consistency of both sub-indices. Cronbach's alpha for the sub-index "sales market" is 0.7450. The "per capita consumer spending" item correlates most strongly with the other components. The alpha coefficient for the sub-index "production site" is 0.8198. The "rule of law" indicator has the strongest correlation with the other items of the sub-index.
The individual indicators correlate with each other, but not excessively, suggesting that the variables measure different statistical dimensions in the data. With a correlation coefficient of 0.7836 at a significance level of 5%, the two indicators "infrastructure quality" and "per capita income" in the "economic conditions" dimension correlate most strongly with each other. With a coefficient of 0.9507, the "corruption" and "rule of law" indicators in the "political conditions" dimension correlate most strongly. In the "social conditions" dimension the strongest correlation is between "education" and "health" (coefficient = 0.7799). With a coefficient of 0.8268, there is a strong correlation between "per capita consumer spending" and "infrastructure quality" in the "sales market" sub-index. The "rule of law" and "labour costs" indicators correlate strongly with a coefficient of 0.7921.
1 For this reason, a principal component analysis appeared relatively meaningless, as it aims to explain the variance of the observed data with a few linear combinations of the original data, i.e to identify the uncorrelated variables, the principal components, which explain a large part of the variance of the data by way of linear combinations (cf. OECD (2008), 63). However, the selected indicators are justified by the theoretical framework in our case and their reduction is therefore undesirable.
2 Cf. Cronbach (1951).
3 Cronbach's alpha measures the degree to which the indicators of a scale relate to each other. The measure rises with the number of items and the covariance of each pair. If the items do not correlate, i.e. the individual indicators are unrelated, Cronbach's alpha equals zero. If there is perfect correlation between the items, the measure is one (cf. OECD (2008), 72)
We conducted an additional test to see by how much Cronbach's alpha varies when one indicator at a time is excluded. A rising Cronbach's alpha after exclusion of an indicator is a sign that this indicator does not correlate highly with the other indicators (cf. OECD (2008), 73). A small increase in Cronbach's alpha was observed for a few indicators. For instance, the measure of the "economic conditions" component rises from 0.7412 to 0.7679 when the item "national debt" is excluded. However, there were usually only minimal variations so that there did not seem to be any need for action, especially since the selection of the indicators is justified by the theoretical framework. It makes more sense to leave a theoretically based variable in the model, even with a small increase in Cronbach's alpha, than to optimise the value of Cronbach's alpha and therefore not consider an important variable any further.
4 Normally, a reliability coefficient of at least 0.70 is regarded as acceptable (cf. Nunnally/Bernstein 1994, 264-265).
5 Per definition, the two indicators are connected with each other. Such a high correlation coefficient is basically rather undesirable. It did seem sensible to use both indicators, though, because they measure different aspects of the same dimension.