# Readiness of Enterprises in Czech Republic to Implement Industry 4.0: Index of Industry 4.0
## 3 Materials and Methods
### Exploratory Factor Analysis  
The factor analysis was chosen to classify the most important variables affecting the level of enterprise readiness for Industry 4.0 into groups. The central aim of factor analysis is the orderly simplification [104] of several interrelated measures using mathematical procedures. The goal of the analysis is to reduce the number of variables through fewer common factors and to reveal the structure of relationships between the variables. Factor analysis in the broad sense comprises both a number of statistical models and a number of simplifying procedures for the approximate description  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Group** & **Category of Group** & **1 st Wave** & **2 nd Wave** \\ \hline \multirow{3}{*}{Size} & Small enterprise (10–49 employees) & 39.0\% & 36.6\% \\  & Medium enterprise (50–249 employees) & 28.7\% & 30.4\% \\  & Large enterprise (over 250 employees) & 32.3\% & 33.0\% \\ \hline \multirow{6}{*}{Technological intensity} & High-tech and medium high-tech intensity (HTI) & 51.2\% & 58.0\% \\  & Of which high-tech sector (HTS) & 7.9\% & 8.9\% \\  & and medium high-tech sector (MHTS) & 43.3\% & 49.1\% \\ \cline{1-1}  & Low-tech and medium low-tech intensity (LTI) & 48.8\% & 42.0\% \\ \cline{1-1}  & Of which low-tech sector (LTS) & 12.2\% & 27.7\% \\ \cline{1-1}  & and medium low-tech sector (MLTS) & 36.6\% & 14.3\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Research sample characteristics.  
of data [105]. The basis of factor analysis is the assumption that the observed covariance (relationships, i.e., correlations) between the variables is the result of the action of common factors and not the interrelationship between the variables. [PERSON] [106] pointed out that the aim of factor analysis is to summarize the interrelationships among the variables in a concise but accurate manner as an aid in conceptualization. Each factor represents an area of generalization that is qualitatively distinct from that represented by any other factor. A measure of the degree of generalizability found between each variable and each factor is calculated and referred to as a factor loading.  
We used exploratory factor analysis (EFA) to explore the main dimensions and generate a new index of Industry 4.0. The scales of the items used in factor analysis were assessed on a scale of 1-4, using the same range as [PERSON] [107] in the survey, to evaluate the Industry 4.0 maturity level of Croatian enterprises. This scale achieved better pilot research results than 1-5 used by [PERSON] [108] or [PERSON] [109] to determine the implementation of different technologies in manufacturing companies.  
The factor analysis helped in particular to determine the internal structure of covariance of variable indexes and to differentiate different groups of the factors. The suitability of data structure for factor analysis was analyzed by [PERSON]'s test of sphericity [110] and the Kaiser-Meyer-Olkin (KMO) test [111]. [PERSON]'s test checked that the observed correlation matrix diverged significantly from the identity matrix at \(\alpha=0.05\) with a \(p\)-value of \(3.021\times 10^{-15}\) (\(\chi^{2}=96.243\), degrees of freedom (df) = 12). Subsequently, the Kaiser-Meyer-Olkin sample adequacy ratio was calculated, and the value was 0.8495. Such a value was deemed high (higher than 0.7), making factor analysis very appropriate [112]. [PERSON] and [PERSON] [113] recommended inspecting the correlation matrix for correlation coefficients over 0.30. Many correlation coefficients do not meet this requirement, but almost all of these coefficients were statistically significant at the level \(\alpha=0.05\).