The Two Step Approach

Another way to build a Higher-Order model is to use the Two Step Ap- proach: the LV scores are initially estimated in a model without the Second- Order construct [2]. Once the First-Order LV scores are computed, they are subsequently used as indicators in a separate higher-order structural model analysis. The First-Order LVs are then a linear combination of the Higher- Order Construct, while the observed variables are directly related only to the specific dimensions. Hence, it is termed a Two Step Approach. This is typical of how analysts previously used factor scores prior to running further regression analyses.

Such an approach may offer advantages when estimating Higher-Order models with formative indicators [28]; [124]. The implementation is not performed through a single PLS run; this implies that any Second-Order

Figure 4.3: Model building: the Two Step Approach

Construct, investigated in stage two, is not taken into account when es- timating LV scores in stage one. The first step of estimation is made by considering only the measurement model which provides the estimation of the First-Order Constructs, as reported in the following equation:

xp,1 = ΛIp,q∗ ξIq,1+ δp,1 (4.4)

In the second step, the estimated scores ˆξI_{, obtained in the first step, are}

used as indicators of the Second-Order Construct:

ˆ

ξ_q,1I =Bq,1∗ ξ1,1II + ζq,1 (4.5)

Sanchez [142] suggests this way of computing scores for the LVs of Lower- Order: we can obtain a score for a First-Order Construct by taking the first principal component of its indicators. Next, the PCA scores of the Lower- Order Constructs are subsequently used as indicators for the Higher-Order Construct in a separate PLS path model.

When using the Two Step Approach, you usually use the mode of measure- ment for the Higher-order Construct in the second stage that matches the construct’s operationalization, (i.e., Mode B for a formative and Mode A for a reflective construct). The Two-Stag Approach has the advantage of es- timating a more parsimonious model on the higher level analysis without needing the Lower-Order Constructs. On the downside, a clear disadvan- tage of any Two Step Approach is that any construct that is investigated in

stage two is not taken into account when estimating the LV scores at stage one. This could encourage “interpretation confounding” [9]; [180]. Simi- lar arguments have followed the use of the Two Step modeling approach advocated by Anderson and Gerbing [3] in the CB-SEM literature. The im- plementation is not one simultaneous PLS run.

Another important difference between the approaches emerges when hi- erarchical LVs are used in a nomological network of LVs as an endoge- nous construct (i.e., a consequence or criterion). When the Repeated Indi- cator Approach is used, regardless of the type of measurement, Mode A or Mode B, and the Higher-Order Construct is formative (i.e., reflective- formative or formative-formative), the Lower-Order constructs already ex- plain all the variance of the Higher-Order Construct (i.e., R2 _{equals 1.0).}

Therefore, other antecedent constructs cannot explain any variance of the Higher-Order Construct and consequently, their paths to the Higher-Order Construct will be zero (non-significant) [73]; [178]. This problem does not occur when the Two Step Approach is used for formative Higher-Order Constructs [73]; [6].

A few studies have focused on a comparison of the two approaches and they are limited to the case of reflective measurements [98]; [180]. From a theoretical perspective, the two approaches lead to different definitions of the Second-Order Construct. The difference lies in the level of the dis- tinction between the measurement and structural models. While in the Repeated Indicators Approach the Higher-Order LV is directly measured by the whole set of MVs (which, in turn, measure the First-Order-specific factors), in the Two-Step Approach the Second-Order Construct is directly measured by means of the First-Order LVs. In the former case, the general construct can be seen as a context variable and its meaning is independent of the relationships with the First-Order Factors. This formalization could apply when, for instance, you want to evaluate the effects of a perception change that had happened in the Second-Order LV on the First-Order LVs or, in the case of formative relationships, the effects of a perception change in the First-Order LVs on the Second-Order LV. Therefore, the Repeated In- dicators Model measures the intensity of the causal relationships between sub-dimensions (the First-Order LVs) and the context. On the contrary,

with the Two Step Approach, the meaning of the Second-Order Construct is defined by the relationships with the sub-dimensions; that is, it is measured and cannot exist before the estimation of the First-Order LVs. The relation- ships reflect, or form, the composition of the Higher-Order LV; indeed, they do not represent how much the First-Order LVs affect the Second-Order LV, but the extent to which the First-Order Constructs reflect, or form, the higher level of abstraction. So, the difference is in the directness of the im- pact of the Second-Order LV on the observed variables. While the Repeated Indicators Approach links directly the Second-Order LV both to the First- Order LVs and the MVs, in the Two Step estimation the general construct has direct effects on the sub-dimensions and only indirect effects on the MVs. In a recent study, Wilson et al. [179] showed that the Second-Order Constructs reliability does not depend on the approach adopted; anyway, the Repeated Indicators Approach produces biased and less consistent es- timates (in the case of small samples) compared to the Two Step Approach.