*2.2. Artificial Neural Network Analysis (ANN)*

PLS-SEM, as well as the other well-known conventional statistical techniques, work exceptionally well when the relationships among variables are linear. As a linear technique, it cannot consider any non-linear effects in the research model, which in some cases could lead to over-simplification and inaccurate results [52]. In order to overcome this potential drawback, ANN models are introduced. ANN is "a massively parallel distributed processor made up of simple processing units, which have a neural propensity for storing experimental knowledge and making it available for use" [53] and it is analogous to the human brain as it learns and stores data through iterative learning process. Artificial neural networks are complex models, classified as artificial intelligence/machine learning techniques, which easily model non-linear relationships [54,55]. In addition, ANN models are also more accurate as compared to the linear models [56] and also more robust and flexible [13,19]. Unfortunately, the ANN approach, due to "black-box" operating nature of ANN models, cannot be used to test of causal relationship among variables [57,58]. Therefore, a hybrid, two-step approach is suggested [16,59]: Firstly, PLS-SEM is used to test hypotheses, i.e., to establish statistically significant predictors of dependent constructs, and, secondly, only significant predictors are utilized as constructs in ANN models. A broad

review of the studies combining SEM and ANN in technology acceptance studies can be found in Kalinic, et al. [60].

Though numerous different types of ANNs exists [60], in this research, feedforward back-propagation multilayer perceptron (MLP) is used as one of the most common and most popular ones [61,62]. An input layer and one or more hidden layers along with an output layer form typical MLP ANN model, while each layer consists of one or more neurons, as presented in Figure 2.

**Figure 2.** An example of MLP ANN.

The number of significant predictors in the model determines the number of neurons in the input layer (i.e., input neurons); while the number of neurons in the output layer (i.e., output neurons) equates the number dependent constructs (outputs) [54,63]. The number of neurons in hidden layer(s) (i.e., hidden neurons) generally depend on the neural network architecture (the numbers of hidden layers, model inputs and outputs), activation functions, sample size, etc., [64] and often is selected using trial-and-error or by simulation software [65].

Input neurons simply accept input signals and forward them to the neurons in the hidden layer. A single neuron is a simple computing unit. First, the weighted sum of all inputs to the neuron is calculated. For example, this sum for the i-th hidden neuron would be:

$$s\_i = \sum\_{j=1}^{n} w\_{i,j} x\_j + b\_i \tag{8}$$

where *xj* is the value of *j*-th input signal, *n* equals the number of inputs, *wi*,*<sup>j</sup>* is synaptic weight connecting *j*-th input with *i*-th hidden neuron, and *bi* is a bias (or a threshold) of *i*-th hidden neuron. The initial values of synaptic weights and biases are set randomly, between 0 and 1, and final values are determined through iterative training process which minimizes cost function, via the backpropagation of error. The output of the hidden neuron is finally calculated by feeding a previously calculated weighted sum through the activation function, which brings nonlinearity to the ANN model. There are different examples of triggering functions (e.g., Rectified Linear Unit—ReLU, hyperbolic tangent), but the most frequently used in the behavioral studies is Sigmoid [60]. Here, the output of the activation function, i.e., the output of *i*-th hidden neuron—*hi* is calculated as:

$$h\_i = \sigma(s\_i) = \frac{1}{1 + e^{-s\_i}} = \frac{1}{1 + e^{-\left(\sum\_{j=1}^n w\_{i,j} \mathbf{x}\_j + b\_i\right)}}\tag{9}$$

where *si* is previously calculated weighted sum of inputs. Although complex ANN models (deep learning) consist of several hidden layers, even ANNs with just the single one can model any continuous function [55] and recent study shows that the most of technology acceptance studies used ANN models with just one hidden layer [60].

The *k*-th neuron in the output layer (in a more general case, with more than one output) calculates the output *yk* of the ANN model in the same way as hidden neurons: as a weighted sum of its inputs (which are the outputs of the hidden neurons), fed through the nonlinear activation function, e.g., sigmoid:

$$y\_k = \sigma(sh\_k) = \frac{1}{1 + e^{-sh\_k}} = \frac{1}{1 + e^{-\left(\sum\_{l=1}^n v\_k j\_l + c\_k\right)}}\tag{10}$$

where *hl* is the output of *l*-th hidden neuron, *m* is the number of hidden neurons, *vk*,*<sup>l</sup>* is synaptic weight connecting *l*-th hidden neuron with *k*-th output, and *ck* is a bias of *k*-th output neuron.

#### *2.3. IPMA*

Standard PLS-SEM studies support details on the relative significance of constructs in the structural model and explains relationships among them. As an alternative to analyzing the importance dimension (i.e., the path coefficients), IPMA examines the performance dimension. IPMA involves five steps [20]. The first step demands checking the fulfilment of the eligibility requirements for performing the analysis. The second step represents the computation of the performance values of the latent variables. To make it possible to interpret the performance levels and to compare them, IPMA rescales indicator scores between 0 and 100 (0—the lowest, 100—the highest). The rescaling of *j*-th observation for indicator *i* (*i* = 1, 2, . . . , *M*) proceeds via:

$$\mathbf{x}\_{ij}^{rescaled} = \frac{E\left(\mathbf{x}\_{ij}\right) - \min(\mathbf{x}\_i)}{\max(\mathbf{x}\_i) - \min(\mathbf{x}\_i)} \times 100\tag{11}$$

In Equation (11) *xi* is the *i*-th indicator, min(*xi*) and max(*xi*) constitute its minimum and maximum value respectively, while *E*(*xij*) constitutes its actual score for respondent *j*. The rescaled construct is the linear combination of both the rescaled indicator's data and the outer weights. The rescaled weights are calculated on the basis of the standardized outer weights of the PLS path model estimation after being unstandardized. The third step involves analysis of the constructs' importance values (i.e., the meaning of construct) that are derived from the total effect (the total sum of all the indirect effects and the direct effects in the structural model [43]). In the fourth step, the creation of the importance–performance map for a chosen construct originates from these previous results using scatter plotting. In the fifth step, IPMA may be expanded on the indicator level to gain accurate data on the highly likely successful managerial measures [20]. IPMA, therefore, extends the results of the standard PLS-SEM method [46].
