Influencing Factors of Catering and Food Service Industry Based on Principal Component Analysis

Scientific analysis of influencing factors is of great importance for the healthy development of catering and food service industry. This study attempts to present a set of critical indicators for evaluating the contribution of influencing factors to catering and food service industry in the particular context of Harbin City, Northeast China. Ten indicators that correlate closely with catering and food service industry were identified and performed by the principal component analysis method using panel data collected from 2000 to 2011. The result showed that three principal components were extracted out of ten indicators, which can be synthesized respectively as comprehensive strength of catering and food service industry, development of social and economy and residents’ consumption willingness to catering services. Additionally, among ten indicators, five relatively important indicators were prioritized as Revenue from principal business of above designated size, Profits of principal business, Cost of principal business, Total investment in fixed assets in hotel and catering services and Retail sales of hotel and catering services.


INTRODUCTION
As an important part of service industry, catering and food service industry is the important carrier of the brand and culture for a country or region with the characteristics of wide market, extensive influence and more employment opportunities.A wide variety of catering products and different styles of food culture has been shaped in the background of different regions and cultures (Yang, 2009).On the other hand, as one of the six elements of tourism activities, "food" has been given to attention by tourists.Catering and food service industry plays an important role in the promotion of local food features and culture of tourism destination through providing catering products and services for tourists.Many countries have designed and developed catering and food brand with own features and style, such as the Beer Festival of Munich in German, Pickled Cabbage Festival in South Korea, series unique meal of cactus and corn in Mexico, Samba Carnival and characteristic barbecue in Brazil and so on.These unique food resources and new product ideas not only attract tourists from all over the world, but also bring considerable catering income (Kang, 2010).
In recent years, the development of global catering and food service industry maintains a rapid and healthy momentum of development (Table 1).According to Fortune Magazine in the United States in July 2012, three food service enterprises enter the world top 500, including American McDonald's Group, the magnate in the snack industry of the world; British Compass Group, one of biggest food group of the world; and Sodexo Group, tourism catering service enterprises in France.Rounding out the top 500 enterprises in the United States was Aramark (the international leading professional company), Yum Brands (the largest network of worldwide restaurants), Starbucks (the leading retailer and roaster of specialty coffee in the world) and Darden Restaurants (the most recognizable and successful brands in full-service dining).These food service groups provide a fast catering and food service for the consumers from more than 100 countries and regions all over the world, accounting for about 5% of global market share (Yang, 2009).It can be seen from Table 1 that the convenience has gradually become the trend of the development of catering market with the rapid development of economy and society.
In China, catering and food industry shows a steady and rapid growth with the rapid growth of Chinese economy and increase of urban and rural residents' incomes since Reformation and Opening.Study area: Harbin is located in the south-central part of Heilongjiang Province, Northeast China, from 44°04′N to 46°40′N and from 125°42′E to 130°10′E, with a total area of 53100 km 2 .Influenced by Chinese traditional food culture and Western food culture, Harbin City has formed a unique food culture and its characteristics can be summarized as "Delicate showed in artless appearance, essence contained in crude style".Some representative foods include northeast stew, timehonored brand snacks, kvass, sausage, bread, popsicles, yogurt and so on.The management forms of catering and food services enterprises is diversified, such as Chinese restaurant, western restaurant, leisure restaurant, fast-food restaurant, cafeteria, chain catering, home-style restaurant and sidewalk snack booth, to meet different levels of consumer demand.A large number of active food enterprises and associations constitute the main body of catering and food services industry in Harbin City.In 2010, there were about 20000 enterprises of hotel and catering services in Harbin City.Among them, 505 corporation enterprises, chain catering and self-employed households of the annual income of main business at and over 2 million Yuan made 5.39 billion Yuan business revenue and 1.08 billion Yuan profits by 31550 engaged persons (Harbin Statistics Bureau, 2001-2012).

Data source:
In accordance with previously studies, this study selected ten indicators related to catering and food service industry and aim to gather an in-depth understanding of influencing factors of the development of catering and food service industry (Table 2).The original data utilized in the analyzing process from 2000 to 2011 were collected from the corresponding Harbin Statistics Bureau (2001Bureau ( -2012)).All the statistical analyses are performed using the Statistical Package for Social Science (SPSS v.20).
Analysis methods: Principal Component Analysis (PCA) is a statistical technique that transforms the original set of inter-correlated variables into a new set of independent uncorrelated variables or principal components.The steps of PCA: (Xu, 2002;Chen and Lin, 2008).
Data pre-processing: In order to eliminate the noise interference caused by different dimensions of the indicators, the original data need to be dealt with.This study standardizes the original data with the following method (Z-score): where, ZX ij = The non-dimensional value processed by standardization X ij = The value of raw data Calculating the correlation matrix: (2) where, r ij (i, j = 1, 2, …, p) is the correlative coefficient between x i and x j of the original variables.The following is the calculation formula: Because R is the real number symmetrical matrix, i.e., r ij = r ji , only the upper or lower triangle elements need to be calculated.

Calculating the variance percentage and the cumulative variance percentage of the principal component:
The variance percentage of principal component (T k ) is calculated: Generally, the first several principal components accounting for 85% of the total variance are retained whilst the rest factors can be omitted in further analysis, that is, the 1, 2, …, m th principal components should accord with D k ≥85% of the corresponding eigenvalues λ 1 , λ 2 , …, λ m (m≤p) (Zhang, 2004;Li, 2008;Shen et al., 2012).

Calculating principal component squared loadings:
The equation is: Then, component score is calculated as follows:

RESULTS AND DISCUSSION
Principal component analysis: According to above research methods, this study analyzed the data sets by virtue of statistical software SPSS 20.The primary results of principal component analysis are presented as follows: KMO test: KMO (Kaiser-Meyer-Olkin) test is used to compare simple correlation coefficients and partial correlation coefficients among the variables.KMO test value ranges from 0 to 1.When it is closer to 1, meaning that the stronger the correlation among the variables, the more suitable the variables are analyzed through PCA.On the contrary, when it is closer to 0, indicating that the weaker the correlation among the variables, the more unsuitable the variables can be used for PCA.The KMO value over 0.6 usually indicates suitability for PCA (Lin, 2007).
According to Table 3, the result of KMO test for all the variables was 0.795, which is suitable for PCA.Similarly, Bartlett's test of sphericity produces a concomitant probability of 0.000, which is less than the significance level of 0.05.Therefore, it is acceptable for the data set to be processed by the PCA method (Shen et al., 2012).

Determination of principal components:
The variances are analyzed with the PCA method and its varimax rotation after KMO test.The explanatory table  4 and 5).Table 4 shows that there are the first 3 principal components whose eigenvalues are bigger than 1 and their rotated cumulative variance have a contribution percentage of 96.85%.Therefore, three synthesized factors out of ten variables were extracted through PCA with the cumulative up to 96.85%.
Table 5 shows the rotated component matrix, where the coefficients refer to the correlations between a principal component and its corresponding variables.The left most column includes ten related indicators.The top row includes three principal components as obtained by PCA.The realistic meaning of a principal component can be synthesized by combining those of the variables which have relatively high coefficients (absolute value) on it.The foremost three principal components, identified by PCA, were thus interpreted as follows (Table 6): The 1 st principal component represents the comprehensive strength of catering and food service industry.Four variables, as shown in Table 6, whose coefficients (absolute value) on this principal component are relatively high among all the variables, are identified to interpret it (Fang et al., 2004).They are, respectively: Revenue from principal business of above designated size (x 8 ) (0.855), Profits of principal business (x 10 ) (0.845), Cost of principal business (x 9 ) (0.821) and Total investment in fixed assets in hotel and catering services (x 5 ) (0.675).The combination of these variables indicates the comprehensive strength of catering and food service industry.

Expression of principal components: Table
Determining relative weights of the principal components is critical to formulate the comprehensive assessment model.In general, the weights can be obtained by calculating the proportion of the corresponding variance to the cumulative variance of all selected principal components (Zhang, 2004;Shen et al., 2012), as shown in Formula (8): where, m is the number of principal components.As a result, the comprehensive assessment model in this study is: Moreover, this study can get the relation between F and the original variables as shown by the equation bellow (Table 8):

Extraction of the relatively important indicators:
In addition, this study respectively uses the importance coefficient of each assessment indicator to minus the mean value (0.056).If the result is larger than 0, it means that the indicator is relatively important; while if it is smaller than 0, it indicates that the indicator is relatively unimportant.
It can be seen from Fig. 1 that 5 indicators consisting of x 5 , x 6 , x 8 , x 9 and x 10 , have importance coefficients that are larger than the mean value, indicating they are relatively important for affecting the development of catering and food service industry.
Comprehensive scores of principal components: At last, standardized data of each indicator are substituted in Formula (10) to calculate the comprehensive scores of principal components for all years 2000-2011 (Table 9).The higher the value, it is shown that the development of catering and food service industry is the better.Principal component --------------------------------------------------------------------Indicator F1 F2 Meanwhile, the final comprehensive scores (∑F) showed an increasing trend, which the development of indicated catering and food service industry keep a good impetus.In terms of own condition, the revenue and profits of catering and food service industry has increased year by year.With respect to the macroscopic circumstances of society and economy, total investment in fixed assets in hotel and catering services showed a trend of substantial increase, from 13.47 million Yuan to 2743.72 million Yuan, approximately 204 times.The retail sales of hotel and catering services increased from 4.13 billion Yuan in 2000 to 27 billion Yuan in 2011.The rapid development of tourism industry attracts a large number of tourists, further drives the development of catering and food service industry.Furthermore, a great change has taken place in residents' consumption structure and consumption demand for catering services has risen sharply.Consequently, these combined factors create favorable circumstances for the development of catering and food service industry in Harbin City.

CONCLUSION
After the analysis of the current situation of catering and food service industry at home and abroad, ten indicators were identified as influencing factors.Furthermore, principal component analysis approach is applied to establish an indicator system for assessing the contribution of influencing factors to catering and food service industry.Finally, a principal component structure consist of three principal components are extracted out of ten indicators, which can be synthesized respectively as comprehensive strength of catering and food service industry, development of social and economy and residents' consumption willingness to catering services.Among ten indicators, five relatively important indicators in terms of catering and food service industry were prioritized as Revenue from principal business of above designated size (x 8 ), Profits of principal business (x 10 ), Cost of principal business (x 9 ), Total investment in fixed assets in hotel and catering services (x 5 ) and Retail sales of hotel and catering services (x 6 ).
The indicators presented in this study have been proved to be reliable and reasonable through a series of statistical analysis.The identified indicators can be adopted to assess the contribution to catering and food service industry.Therefore, it is concluded that principal component analysis method have great application potential for better understanding of influencing factors of catering and food service industry.

Table 1 :
Survey of global main food services groups (issue date: May 21, 2012)

Table 2 :
The original data of ten indicators related to catering and food service industry in Harbin City

Table 3 :
Results of KMO and Bartlett's test

Table 4 :
Total variance explained

Table 5 :
Rotated component matrix Principal

Table 6 :
Explanation of the principal components

Table 8 :
The importance coefficient of assessment indicators