6. Factor and Cluster Analyses

To perform the cluster analysis, we should take individuals answers to the questions concerning «Health» category: l5_0_(Number of visits to the doctor), l5_(Did you have any health problems during the last 30 days?), l20_(Were you in a hospital during the last 3 months?), m71_(Do you smoke now?), alclast30 (Did you consume alcohol during the last 30 days?), m11311a_(Did you go to fitness in the last 30 days?), m113_1a_(Did you run in the last 30 days?), m113_2a_(Did you swim in the last 30 days?), m113_3a_(Did you dance in the last 30 days?), m113_4a_(Did you play basketball or football in the last 30 days?), m114_(Which variants of the descriptions does fit your behavior better?), l31_(Did you miss your work during the last 30 days due to illness?), m1_(Weight), m2_1_(How have your weight been changed over the last year?). For conducting the cluster analysis 14 explanatory variables are taken. However, it is no reasonable to make the cluster analysis on these 14 variables since many variables such as l5_0_(Number of visits to the doctor) and l5_ (Did you have any health problems during the last 30 days?) correlate with each other. As in our analysis we should include variables that do not correlate with each other.

Table 7. Correlation Matrix

The way to solve this type of problem is to use PCA Factor Analysis. The factor analysis is a way to reduce the dimensions and quantity of variables. It also solves a problem of finding an allocation of only significant variables that make influence on dependent variables;

It is assumed that the observed variables are just a linear combination of some unobservable factors. It facilitates the solution of the multicollinearity problem in the model in the number of ways. Firstly, the factor analysis reduces the quantity of variables (creating a Factor or a Principal Component, in other words a «pool» of similar variables) Secondly, it also provides possibility of rotation of Factors or Principal Components so that we can use uncorrelated factors in the model.

Next step is to perform the factor analysis. To determine the number of factors that are needed to be selected, we should carefully examine the «Cumulative column». As it was mentioned in the methodology part on the research, in order to define the number of factors that will be used for modeling, we should select all the values that do not exceed 0.8.

Table 8. Factors

According to the criteria described above we should select 9 factors. However, we assume that these factors are dependent. Therefore, we perform the orthogonalization (rotation) of factors in order to obtain factors that are independent between each other. As a result of the orthogonalization we obtain four independent factors. The following task is to interpret their meaning. In the table below we can observe factor loading matrix containing the correlation between factors and initial variables responsible for determination of lifestyle type.

Table 9. Factor loading matrix

We can observe from the Table 9 that the first factor correlates mostly with questions about sports (running, swimming, fitness, football/basketball) and with the answer to the question how often the respondent does sports. The second factor is correlated with the answers concerning questions of visiting the hospital, if he stayed at the hospital, absenteeism of work due to illnesses. The third correlates with smoking and drinking some alcohol. The fourth is correlated with dancing and body weight.

On the basis of this information, we can interpret the obtained factors in the following way. The first factor is responsible for sports, the second one - for health, the third one - for bad habits. Factor four is harder to interpret, however it can be considered as responsible for leisure time.

Based on the factor analysis, the cluster analysis is conducted. Since respondents do not answer all the questions, there is a large number of missing values, therefore it is not possible to create cluster analysis based on answers of all 1132 of respondents as a panel data analysis. The way to solve this problem is to perform the cluster analysis on results of the factor analysis for the entire sample from 2005 to 2012.

We should make a selection number of clusters according to the method of single linkage, using Calinski statistics. (Appendix 8)

We can see that there is a break for 3 and 4 clusters. The highest VRC ratio is reached when the number of clusters is equal to 4. We have tried to conduct the research using 4 different clusters, but this attempt has not been successful. In case the sample was divided into 4 clusters it was quite hard to interpret them as they were close to each other in terms of characteristics of health condition. The variation between clusters was insufficient which is unacceptable for the purpose of our research. So, we decided to divide our sample into 3 clusters to obtain more pronounced differences between them.

Besides, it should be stated that the sample used in the research is scarce and include only 1 919 respondents' answers. This is another reason to use 3 clusters instead of 4. In case of 3 clusters we are able to provide proper interpretation of all the clusters that are used in the paper and obtain proper amount of observations in each cluster.

The cross table 10 given above provides insight into respondents' answers about their self-assessment of their health status according to the formed cluster. We use Сhi2 statistics to make sure that interconnection between the cluster number and level of health can be interpreted. However, at this point we are not able to make definite conclusion about the meaning of the clusters. Probably, this question cannot be considered as a solid indicator of person's health condition due to the fact that self-evaluation is not always a correct estimation of actual health. In other words, the person might believe that he is healthy despite the fact that he or she suffers from a numerous diseases. That is why we need to examine the distribution of the answers according to other questions in order to get an adequate description of the clusters.

From the table 11, based on Chi2 statistics, we may find out that the interrelationship between the number of the cluster and health status exists. We can observe that in the first cluster we have 718 respondents (who represent 91% of the cluster) that provided the answer that they did not have health problems in the last 30 days, whereas in the third cluster 283 people (79% of the cluster) said that they had problems with their health. This implies that the first cluster represents people with good health status, the third cluster has people with poor level of health and the second cluster is neutral. However, neutral cluster is closer to the first one, characterized by better state of health condition, as the number of respondents that say that they had no problems is 618 (81%), which is not significantly lower than 91% in the first cluster. At this point it could be assumed that we have formed the following clusters:

1) Cluster 1 - people with good health condition;

2) Cluster 2 - people with neutral health condition;

3) Cluster 3 - people with poor health condition.

Firstly I would like to examine interconnections between clusters and qualitative variables. In order to perform this relationship, we build a cross tabulation matrix that shows interdependence between the number of a cluster and a qualitative variable. The results are presented in Appendices 2, 3 and 4. Based on the information provided in the Appendices, we found out that variables such as: marital status, level of education and gender are significant. We have discussed qualitative analysis and now we would like to give descriptive statistics of quantitative variables. From Appendices 5,6 and 7 we observe that in cluster 1 the average weight of respondents is 63 kilograms and the average age is 25 years old. In cluster 2 we find out that average age of participants is 29 years old, while average weight of a respondent od 78. What concerns cluster 3, the average weight is equal to 64 kilograms ant average age of a respondent is 26.

It should be also noted that we conducted a Chi2 test to define the relationship of attributes to different variables. Chi2 test evaluates the hypothesis that there is no relationship between the variables. If p-value is less than 0.05, then we reject the null hypothesis and claim that the relationship between the variables could be interpreted. In our case p-value is equal to 0.000, so we may make assumptions about the number of a cluster and answers of respondents concerning diseases in the last 30 days.

Next we are going to examine relationship between clusters and day that people skip at work due to illnesses.

According to information provided in the table 14, 99% of observations in cluster 1 did not miss the work due to illnesses in the last 30 days. Simultaneously cluster 3 represents observations (more than 35%) that have connection to the recent health issues. Based on Chi2 statistics we may conclude that interrelationship between the number of the cluster and missed days at work exists. As a result we can make an assumption that the cluster structure that has been detected earlier is adequate.

The information in the table 13 provides characteristic whether the person has spent time in the hospital in last 3 month or not. According to Chi2 statistics we discover that interrelationship between these variables exist. We can clearly observe that the number of positive answers in cluster 3 is almost 6 times higher than in cluster 1. Additionally the share of observation that corresponds with negative answer to the question about spending time in the hospital is much higher in cluster 1 than in cluster 3. As a result, we can assume that it is another point that proves the cluster structure that has been stated earlier in the text.

However, the only cluster analysis is not enough to identify trends. It is interesting to find out how the individual's match to a particular cluster would change if, for example, the marital status transformed, a person got higher level of education or gained weight and so on. We run a multinomial logistic regression in order to find interdependencies between the cluster number and gender, age, martial status, level of education and weight.

The number of a cluster is taken as a dependent variable (1 cluster - good, 2 cluster - neutral, 3 cluster - poor). Age, gender, weight, martial status and level of education are taken as independent variables to test the afforested hypotheses. So, we run a multinomial logit regression and assume that the second (neutral) cluster is the base one.

The next section contains the description of results concerning the impact of various characteristics of respondents on their lifestyle.

7. Estimation Results

Conclusion

The aim of our research was to find out what variables affects the probability of getting into a particular health status cluster. While conducting the research, we detected four significant variables that play an important role in defining which type of lifestyle to choose. Also, we detected the following hypotheses. The first one states whether health status deteriorates with age, the second one tries to find out how weight affect health status, the third one deducted that women tend to be healthier than men, the forth one tries to explain how the education level makes influence on health, while the last one tries to determine whether the marital status is significant in leading a healthy lifestyle.

In our research we took the data which contains people aged from 14 to 40. The reason we specify the selection in such a way is due to the fact that after 40 people start having health problems that arise due to the age and might have nothing in common with the lifestyle patterns that the person has. The data grants evidence that people aged 26-30 provide the majority of answers to the questionnaire. We believe that people of that age are actively interested in their health and willing to find out ways staying healthy as they get older.

In our analysis, we firstly conducted factors that helped us to perform the clusters. We had four factors that were responsible for sports, bad habits, leisure time and health. After that we build three main clusters that reflect the type of a healthy lifestyle. Cluster number one stays for good health status, the second one was neutral and the third one was for the poor state of health. So then we build a multinomial regression model and get the following results.

We came to the conclusion that higher level of education does not helps people to stick to a healthy lifestyle that can be described as people that are more educated tend to do have jobs that does not require physical activities that negatively affects their lifestyle patterns. Also we have discovered that an increase in age does not play a negative role in human's health due to the fact that people tend to pay more attention to their health as they get older. What is more, it was concluded that men tend to lead healthier lifestyle than women as we assume that they are not influenced by different diet tendencies. These days women care mostly about numbers on weight rather than overall health status. Moreover, we deducted that an increase in weight does not provide significant effect on the health status of the person.

In addition, based on the results we received in the research we may say that hypothesis concerning marital status has not been rejected. We assumed that married people tend to lead a healthier lifestyle. However, while running the regression we discovered that this variable is not significant for cluster that describes poor state of health, whereas significant for the cluster that describes a good state of health.

Nowadays it seems essential that healthy lifestyle is a key to long and prosper life. Unfortunately, a large number of people tend to understand this idea but do not put it in practice. It is believed that a person has to spend a vast majority of his or her time doing sport and miss out on tasty nutrition. However, it is not always the case. If the person is willing to maintain healthy state of body, he or she does not have to be a diet expert or professional football player. One just needs to pay attention to what he or she eats and avoids sedentary lifestyle.

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