The Reproduction of Hofstede Model

G. H. Hofstede (1980) Culture's Consequences is a result of an extensive research on the international comparison of corporate culture in 40 countries through 1967 to 1973. Hofstede identified four dimensions of culture from the investigation data of IBM's 40 subsidiaries. He developed four indices, but did not explicitly present the exact computation formulas for Individualism index and Masculinity index. This paper reproduces the formulas and proves how to conduct a factor analysis that Hofstede employed for development of these indices. Hereafter, supplementary analysis could be done using all four indices of Hofstede. Also a factor analysis could be done in Hofstede's method.


Introduction
analysis, but Hofstede (1980) did not explicitly present the exact computation formula (Takahashi, 1995, chap. 5). The detail on the computation formula is reviewed hereafter.

PDI (Power Distance Index)
Power Distance is a measure of the interpersonal power distance between B (boss) and S (subordinate), which is defined as "the difference between the extent to which B can determine the behavior of S and the extent to which S can determine the behavior of B" (Hofstede, 1984, p. 72). In actual analysis, PDI is employed so that it becomes higher when the followings become high: (1) Frequency of employees' perception that they are afraid to disagree with their managers.
(2) The ratio of those subordinates who prefer not to work for superiors with a consultative style of decision making. (3) The ratio of those subordinates who perceive their boss as autocratic or persuasive.
By definition, the higher PDI is, the higher Power Distance becomes. The formula used is as follows: The constant 135 has been added to give the index value a certain range.  (Hofstede, 1980, pp. 403-410).

UAI (Uncertainty Avoidance Index)
As for Avoidance of Uncertainty, UAI is employed which is designed to become higher when the followings become high: (1) The degree the employees considering that company rules should not be broken even if they think it is not in the company's best interests.
(2) The ratio of those who believe to continue working with the present company more than another five years. (3) Frequency they feel nervous or tense at work.
"Stress" question is introduced in (3) since following relations are observed in which (3) relates to (1) and (2); two means to avoid uncertainties, via the anxiety level and the desire for safety: (3) anxiety level desire for safety (1) and (2) The used formula is as follows: The actual range of UAI is 8 UAI 112, while its theoretical range is -150 UAI 230. UAI was correlated to the average age of the respondents.
UAI has been compiled on the basis of the country mean scores for three questions, that is, B60 (rule orientation) and A43 (continue working less than five years) as well as A37 (nervous/tense at work) which is relative to the former two variables.

IDV (Individualism Index) and MAS (Masculinity Index)
As for IDV and MAS, though a factor analysis was used for the development of the indices, how to calculate them has not practically been explained (Takahashi, 1995). Though the research of Hofstede is known very well, a supplementary examination by third party researchers in the strict meaning has not been done so far. We intend to follow the analysis of Hofstede as requested in Fujita (1999) which gave the first explanation on how to calculate these two indices.
Hofstede conducted a factor analysis on the basis of the mean scores of every country computed from 14 "work goals" questions. Then he focused on two main factors that could explain 46% of the variance of the mean scores, and related the first factor to the degree of individualism, and second factor to the degree of masculinity. The first factor was named "individual-collective" factor because it opposed goals that did not stress independence from the organization to goals that stressed independence (Hofstede, 1980, pp. 220-221). The second factor was named "social-ego" factor because it was characterized by high importance of manager and cooperation, and low importance of earnings (Hofstede, 1980, p. 277). By substituting the factor scores (INV, SOC) of these two factors for the following formulas, IDV and MAS are calculated so that the value of the indices may be within range UAI=300 -30×B60 (mean) Rule orientation -A43 (1+2: %) -40×A37 (mean) Continue working less than five years Nervous/ tense at work between 0 and 100 (Hofstede, 1980, pp. 242, 299).  Table 3). Therefore the factor structure in "work goals" questions is not clear.

Reproduction of IDV and MAS
As mentioned above, two versions exist in Culture's Consequences, one is 1980 version, which is the first edition, and the other is 1984 version, which is the abridged edition. Descriptions on the statistics and so on used for the analysis of IBM data are removed from 1984 version. Even though the analysis made in Cultures and Organizations (Hofstede, 1991), to which data in 13 countries were added newly, is the same, descriptions on statistics is much simpler.
Four dimensions of culture were identified in IBM data, that is, PDI, UAI, IDV, and MAS. How to calculate PDI and IDV was made clear, and also the computation formulas were mentioned explicitly.
However, from reasons stated above, not only the computation formulas of the factor scores needed for calculating IDV and MAS but also the method of factor analysis used to develop the indices were not explained. Table 1  What Hofstede did not refer is (1) how to read the simple totals of "work goals" questions, (2) the summary of factor analysis on "work goals" questions, (3) the interpretations of the factors extracted from the factor analysis. These three points are cleared in the following.

How to Read the Simple Totals
The simple totals of 14 "work goals" questions appear on   (Hofstede, 1980, pp. 79-80).
As a matter of fact, the latter half of this operation is substantially the same as the calculation of deviation value. Though deviation value is 50  Each mean score is reversed Likert scale, thus it is possible to get raw data mean by subtracting from 6.

Summary of Factor Analysis
The factor scores calculated from factor analysis on 14 "work goals" questions are used to compute IDV and MAS. The procedure for this factor analysis is mentioned in the statistical analysis section of the 5th chapter (Hofstede, 1980, pp. 237-259).
Not the numerical values themselves of the answer but the standardized values from following process are used in factor analysis. First, the values of "work goals" questions are averaged by seven types of job in every country, then they are standardized. Every country's standard scores are mean of these seven standard scores (Hofstede, 1980, pp. 78, 237, note 19 in p. 90).
Hofstede conducted a factor analysis on the basis of 40 countries 14 questions matrix (Hofstede, 1980, p. 241 (1980). Because an initial factor method was not presented clearly, the factor analysis was done with both principal components method and principal factors method. As a result of the factor analysis, not only factor scores but also factor loadings and standardized scoring coefficients of all the questions were computed (Table 2: but only the factor score SOC is multiplied by minus 1 in accordance with Hofstede).
Signs were opposite when factor scores were compared before and after the reverse of Likert scale.
Though the signs of standard scores and factor scores are reversed by the reverse of Likert scale, it is confirmed that Hofstede conducted a factor analysis on the standard scores of raw data because the factor scores before reverse are same as those in  indicated that the first factor was related to "collectivism" and the second factor to "femininity." The factor structure of these two factors is reinterpreted here.
Therefore the first factor's characteristics become stronger as the degree of dependence to the company increases and cooperation is placed importance, while weaker as personal interest and respect for privacy are valued. The first factor has the confrontation structure of "collective-individual" because strong loyalty to company organization and emphasis on group harmony are the expressions of collectivism. The higher the degree of collectivism is, the higher the factor scores of the first factor are. It was revealed that Hofstede multiplied factor loadings and standardized scoring coefficients by minus 1 and interpreted the first factor as a factor of individualism.
Second, the factor loadings of the second factor (Table 2) are examined. Hofstede conducted the following analysis prior to the interpretation that the second factor was related to "masculinity." This analysis aims at confirming whether there is any difference between men and women concerning importance placed on different work goals. He selected occupations that have sufficient numbers of employees of both gender to allow statistical treatment of data, and where employees of both gender engage in equal tasks. A t-test between men and women was done on the basis of the mean scores of "work goals" questions (Hofstede, 1980, pp. 271-275). Result is in Table 3.
The questions that have positive factor loading are "Cooperation" (A8), "Manager" (A16), "Desirable area" (A6), and "Employment security" (A14). The questions that have negative factor loading are "Earnings" (A7), "Recognition" (A11), "Advancement" (A15), "Challenge" (A5), and "Use of skills" (A17), absolute value of factor loading being higher respectively. When this is compared with Table 3, it is understood that the higher the scores of "work goals" which women place importance, the higher the factor scores of the second factor. It is proved that Hofstede formulated the index as "masculinity" by multiplying factor score by minus 1 in consideration of the larger number of male respondents (Hofstede, 1980, p. 277). However, essentially, the second factor should be related to "femininity."

For Further Supplementary
Examination Based on the above analysis, data treatment process in supplementary examination by using IDV and MAS will be explained. Analysis can be performed in two ways. One is to compare the culture internationally or to examine diachronic change of culture in comparison with IBM data by using the calculation formulas of two indices that Hofstede developed. Another is to verify the validity of these two indices or to develop a new index of culture by using factor analysis as Hofstede's.

Using Two Indices in Original Form
When using the computation formulas of IDV and MAS developed by Hofstede in original form, answers for "work goals" questions must be collected and factor scores should be estimated from that data. First, it is needed to calculate the following two kinds of mean scores and standard deviations of each "work goals" question. One kind is the mean scores of each question calculated for the country.

Conducting Factor Analysis
When conducting the same factor analysis as Hofstede, it is necessary to calculate the correlation matrix of "work goals" questions. Then calculate the eigenvalues of this matrix, and conduct a factor analysis using the number of eigenvalues above 1 as factor number criterion. In fact, this correlation matrix is computed in the process of principal component analysis. Therefore conduct a factor analysis employing principal component method as initial factor method. That is, the factor analysis of principal component method using varimax rotation as rotation method is needed.
The data used in factor analysis of Hofstede (1980) is standardized. Yet it is required to conduct a factor analysis with raw data because standardization is automatically processed in general factor analysis programs.
Next, compare the rotated factor pattern computed from the factor analysis with the factor loadings shown in Table 2. It can be said that the factor of "collectivism" and "femininity" were extracted if the number of factors extracted and the signs/amount of factor loadings were about the same as in Table 2. In that case, simply multiply the second factor by minus 1 and substitute the factor scores into the computation formulas shown in above section .
When the signs/amount of factor loadings do not align with Table 2, interpret what the factors extracted are. The way of analyzing a factor structure is to pick out in order from the higher factor loadings and classify them by plus and minus, then examine what kind of confrontation structure they have.