## The Quality of a Composite Score of a Concept with Formative Indicators

Complex concepts with formative indicators are latent variables that are determined by different causes of the latent variable. Job satisfaction again can be used as an example to make it clear what the difference is between the complex concept with reflective and formative indicators.

If Job satisfaction is a complex concept with formative indicators, these indicators are causes of the general job satisfaction. The indicators could be satisfaction with different aspects of the work such as: the work one has to do, the social contacts, the working hours, the spare time etc. All these indicators can be causes for the latent variable Job satisfaction. Therefore this model is very different from the model for concepts with reflective indicators. Also in this case the measure for the latent variable is a weighted sum of the answers of the different indicators. However in contrast with the other two complex concepts the way to determine the quality of this complex concept is not yet clear as will be indicated below.

The figure presents a measurement model of a complex concept with three formative indicators.

If Job satisfaction is a complex concept with formative indicators, these indicators are causes of the general job satisfaction. The indicators could be satisfaction with different aspects of the work such as: the work one has to do, the social contacts, the working hours, the spare time etc. All these indicators can be causes for the latent variable Job satisfaction. Therefore this model is very different from the model for concepts with reflective indicators. Also in this case the measure for the latent variable is a weighted sum of the answers of the different indicators. However in contrast with the other two complex concepts the way to determine the quality of this complex concept is not yet clear as will be indicated below.

The figure presents a measurement model of a complex concept with three formative indicators.

The major difference between formative and reflective indicators comes from the nature and direction of the relationships between the latent complex concepts and their indicators. In case of formative indicators the arrows go from the indicator variables to the complex concept. The consequence is that the effects of the indicators on the complex concept can´t be estimated because the dependent variable is not measured even if the correlations between the latent variables of the indicators are known. A model with latent dependent variable is by definition not identified.

Several solutions have been suggested for this problem (Bollen et al. 2018) but there remain many unsolved problems

Given that we don´t see a solution for these problems, we think that we have to conclude that we can´t specify an acceptable approach for the estimation of the quality of measures for complex concepts defined by formative indicators at this point in time. Further research is needed.

However when the effects of the different aspects of the concept with formative indicators has been determined the evaluation of the quality of the composite score is the same as for the simple sum composite score.

Several solutions have been suggested for this problem (Bollen et al. 2018) but there remain many unsolved problems

- The effect coefficient in the model can only be estimated if one adds to the model extra dependent variables. But with the choice of these variables the causal effects will vary and so the relationships between the latent variable of interest and the composite score obtained for this variable will vary too.
- If the complex concept really exist which is true for concepts like Job satisfaction, the best dependent variables to use to make the estimation of the effects of the indicators possible would be two or more reflective indicators.

Given that we don´t see a solution for these problems, we think that we have to conclude that we can´t specify an acceptable approach for the estimation of the quality of measures for complex concepts defined by formative indicators at this point in time. Further research is needed.

However when the effects of the different aspects of the concept with formative indicators has been determined the evaluation of the quality of the composite score is the same as for the simple sum composite score.