Definition of Invariance (of Measurement)

It is a technique that aims to compare groups and determine if a construct has the same meaning for different groups or samples; this is achieved by the gradual inclusion of equality constraints.

One of the most recurring questions in the investigation is Can we assume that our results are the same for all people? There will be occasions when the characteristics of the participants can alter the relationships between the variables. For example, a study carried out in the United States determined that having clinical breast examinations is determined by the emotions associated (fear, anxiety and shame), fatalistic beliefs and some structural variables such as age, education or economic income, however, these relationships are different for Latina women and Anglo women.

If we wanted to replicate this study, but addressing the STI test and comparing the results between men and women, how would we do it? The first option would be analyze the relationships separately and then compare the previously standardized results; although this would be quite impractical. Fortunately, structural equation modeling (SEM) has a more practical option, analysis of invariance, which aims to

determine whether the relationships or, rather, the parameters of a model are maintained or modified based on the creation (or selection) of groups with certain characteristics (for example, male-female, heterosexual-homosexual, white-Afro-descendants).

Although the analysis of invariance or measurement invariance commonly performed by Confirmatory Factor Analysis (CFA), all techniques derived from SEM are able to perform analysis of invariance. Thus, in the analysis of invariance, it is investigated whether the operationalization of a construct has the same meaning under different conditions (characteristics of the sample, method of administration of the construct, the time of administration). The absence of measurement invariance would indicate that a construct is ambiguous under the established conditions. In this sense, it is also possible to speak of longitudinal measurement invariance, which is carried out with the same conditions, but at different times and assumes that a construct is the same despite the passage of time. time.

As mentioned before, to carry out the analysis of measurement invariance, one gradually adds constraints to the model parameters, these constraints name four possible levels of invariance that can be they can get. These levels are described below, however, it is necessary to mention that the authors do not always use the same name.

• Baseline model. In a strict sense, this is not a level of invariance, since before applying any restriction, it must be tested whether the hypothesized model for each group has a good fit.

• configural invariance. It determines that each group has the same configuration, that is, that they have the same indicators in both groups. If the configural invariance is not reached, none of the following levels can be achieved either.

• weak invariance. At this level it is assumed that configural invariance has been achieved. Therefore, we proceed to establish restrictions of equality in each indicator of the model for both groups.

• strong invariance. At this level it is assumed that weak invariance has been achieved. It requires that equality constraints be applied to all intercepts of the model. The intercept refers to the score of each indicator, therefore, this level of invariance would indicate that both groups responded in the same way to the constructs.

• strict invariance. It is the highest level of measurement invariance, and assumes that strong invariance has been met. This level includes restrictions on errors and covariances between groups. Therefore, this level would indicate that the construct is identical in both groups.

• When you have structural equation models or path models, it is possible to have an extra level of invariance, structural invariance. At this level, restrictions are established on the relationships between the variables or structural paths. So reaching this level of invariance would indicate that the phenomenon occurs in the same way in both groups.

In order to assume that a certain level of invariance has been met, the fit of the model must be compared with respect to the previous level (for example, the model of strict invariance with the strong invariance model), if the fit does not worsen, it is assumed that the model is invariant and it can continue with the following level. In this sense, different criteria have been proposed for this process, but the most usual is to compare the chi-square, CFI and RMSEA values.