**4. Methodology**

To describe the trend behaviour of these islands, we have considered some statistical indicators taken from the literature that refers to some macroeconomic dimensions (Table 4). The main supply and demand data for EU islands analysed come from Eurostat and the Observatory of Tourism for Islands Economies (OTIE). The variables consider the evolutionary trend over ten years from 2010 to 2019. The first two variables (variation of the number of hotel accommodations and variation of the number of non-hotel accommodations) measure the increase in the number of hotels and non-hotels during the observation period (Ruggieri and Calò 2022). According to Eurostat, we consider holiday and other short-stay accommodations, camping grounds, recreational vehicle parks, and trailer parks

in the non-hotels categories. These variables are relevant to describe the tourism sector evolution because the accommodation establishments, according to the United Nations World Tourism Organization (UNWTO) statistical convention, are the essential elements of the existence of tourism products.


**Table 4.** List of variables used.

Source: data analysis on OTIE Islands database.

The development of new hotel structures demonstrates the existence of a growing tourism supply and the possibility of containing the increasing tourist demand. Hotel facilities represent essential investments in the territory and have a multiplier effect on economic development and island sustainability. In contrast, non-hotel facilities, on the other hand, are a quick way to meet demand needs. Significant investments are unnecessary in some cases (use of second homes), and the impact on the island's sustainability could be contained or limited. The third and the fourth variables (variation of the population and employer variation) measure the attractiveness of the islands from a social and economic point of view, and it will be used as an attractiveness proxy. When an island has development growth, we expect an increase in employment followed by population growth. The decline of the population and islands is a much-discussed topic in the literature and has been addressed by local governments for several years. Population decline involves reducing community services (think of the closure of hospitals or parts of them) and less social capital (the ageing population).

Finally, the last variable is related to the characteristics of the tourism sector. The dimension associated with international arrivals highlights the interests of the global tourism market for the island. As already stated, all these variables are considered in their evolution in the same observation period. To avoid the danger of overestimation, the starting value of each variable corresponds to the average of the values for the years 2010 and 2011. Similarly, the end-of-period values correspond to the average values for 2018 and 2019. Therefore, their value is a trend linked to territorial transformation paths.

Factor analysis was carried out to analyse the relationships between the five variables. Factor analysis (FA) is a method to analyse the interrelationship within a group of variables and identify some factors believed to contain basic information about the observed structure. This methodology explains the correlation between the observed variables due to fewer non-observed factors. These factors are also known as "components", "dimensions", or "latent factors". Furthermore, the agglomeration of observations is transformed into a simple structure that can "inform" as much as the initial setup (Mignami and Montanari 1994). Of all the techniques of multivariate analysis, FA is of the most significant interest because of its possible application in the business sphere, particularly regarding market research (Iacobucci 1996; Cool and Henderson 1997). Finally, the applied methodology finds the main factors that can identify the two island groups based on chosen variables from the two theoretical models.

Applying the methodology to such a small sample requires caution in interpreting the results. Several contributions in the literature discourage researchers from using FA when their sample size (N) is too small. Some authors, such as Guilford (1954) and Cattell (1978), recommend a minimum sample size of 200. Other researchers have focused on the number of cases per variable (N/p) (Hair et al. 1979). However, as de Winter et al. (2009) recalled, the absolute N and N/p ratio recommendations were gradually abandoned as erroneous.

Recently, studies have shown that the minimum sample size is a function of several parameters (Gagné and Hancock 2006; MacCallum et al. 2001; MacCallum et al. 1999; Velicer and Fava 1998).

On the other hand, some studies have shown the application of factor analysis to very small samples (Velicer and Fava 1998; Geweke and Singleton 1980; Bearden et al. 1982; Preacher and MacCallum 2002), considering them to be adequate. Aware of these limitations, we used factorial analysis for our study.
