4. FACTOR ANALYSIS

4.1 Definition

The common factor analysis procedure is briefly described below. For a thorough description of factor analysis see Rummel (1970). In the procedure, each variable is assumed to be a linear combination of some number of common factors and a unique factor:

Zj = [SIGMA]k(ajkSk) + ajuSju

where

Z - standardized variable,

a - factor loading,

S - common factor or factor score,

j - index for variables,

k - index for factors, and

u - denotes the unique portion.

Rmxm - Imxm + H^2mxm = Fmxp F'pxm

where

Rmxm - correlation matrix,

Imxm - identity matrix,

H^2mxm - diagonal matrix of communalities,

Fmxp - factor loadings (a) matrix,

F'pxm - transpose of F,

m - number of variables, and

p - number of factors.

h^2j = [SIGMA]k a^2jk and
u^2j = a^2ju.

4.2 Methods

A fundamental problem concerns the formation of the factor structure. While the variables to be factor analyzed must be correlated in some way, researchers are divided over how the variables should be related to each other. Mulaik (1993) suggests that the factor structures based on theory should be set up prior to conducting a factor analysis which would prove or disprove that theory. On the other hand, Velicer and Jackson (1990) state that both confirmatory and exploratory analysis, the latter occurs when factor structures are based on data, have important roles to fill. In the factor analyses presented in this study, survey questions were designed to incorporate the drives and constraints from telecommuting decision theory (section 2.3). However, the nature of the research itself is exploratory, so the data ultimately suggests the factor structure.

Researchers have also given guidelines for the minimum sample size needed to conduct factor analysis. Some have suggested the ratio of sample size to number of variables as a criteria: the recommendations range from 2:1 through 20:1. Others have suggested a minimum sample size of 100 to 200 observations (Guadagnoli and Velicer 1988). Guadagnoli and Velicer (1988) found that absolute sample size was more important than functions of sample size in determining stable solutions. Small sample sizes may affect the factor analysis by making the solution unstable: the addition of more data may cause the variables to switch from one factor to another (Guadagnoli and Velicer 1988). For the set of questions from part B, the ratio of sample size to the number of variables is 8.8:1 for the solution shown in section 4.3. However, the sample size of 97 lies just below the suggested minimum sample size which indicates that the small sample size may be a problem. For the part C questions, the ratio is 9.7:1 and the sample size is 291 due to the rearrangement of the data (see section 4.4), so sample size effects are not likely to be present.

Although there is little missing data (0.5% and 0.8% of the responses are missing for the job satisfaction and work attitudes questions, respectively), the handling of the missing information may affect the factor analysis procedure. Most of the missing data in parts B and C was caused by respondents incorrectly interpreting the instructions and failing to answer each question for all three workplaces. SPSS/PC+ provides two options for handling missing data: mean substitution and pairwise deletion. For mean substitution, the missing value is replaced by the average value for the sample. In pairwise deletion, the correlation coefficients are calculated using only the valid data, thereby retaining much of the information that would have been lost by deleting each case that had missing data. Although a few of the solutions calculated using pairwise deletion looked promising, the computer package did not allow the saving of factor scores when using this procedure. As a result, mean substitution was used to replace the missing data.

In each group of questions, there are two questions that provide a "not applicable" response. For the job satisfaction group, the questions refer to clients (B3F) and supervising of others (B3M), and for the work attitudes, the questions ask about dependent care (C21) and household activities (C23). Originally, responses are coded 1 through 5 from "strongly disagree" to "strongly agree" with the not applicable response coded as a 6. If the value of 6 were retained, those selecting not applicable would be seen as agreeing with the statement more strongly than those marking "strongly agree". The three possible methods to deal with this problem are to recode the not applicable response as neutral (which has the value of 3), to substitute with the mean, or to exclude the questions from the factor analysis. Recoding as neutral has some theoretical validity because if the question does not apply to the respondent, s/he would likely have neither a positive nor a negative opinion about it. However, this will reduce the variation in responses to these questions since more responses would be grouped near the middle of the scale. As a result, the significance of the strong opinions of those who did express an attitude may be reduced. Using means substitution would treat the not applicable responses as missing data. Unfortunately, this approach also reduces the variation in response and has the additional effect of supplying the "not applicable" respondents with an non-neutral opinion. Removing the not applicable questions from the factor analysis altogether may lead to less interpretable factor structures and/or diminish the completeness of the common factor space. For the job satisfaction questions, excluding the not applicable questions provided the most interpretable factor solution. However, for the work attitudes questions, the factor solutions with the not applicable response recoded as neutral provided more interpretable factors (and appeared logical), so the recoding method was chosen instead.

Two common methods of factor extraction are principal component analysis and principal axis factoring. In the first method, the communality (h^2) is assumed to equal one, and, therefore, the uniqueness is equal to zero (see above). This is simply a linear transformation of the variables that assumes the factors will explain all of the variance in each variable. The second method, on the other hand, relaxes this assumption and allows the unique portion to be non-zero. As a result, the factor loadings are higher which leads to greater interpretability since the unique portion does not have to be taken into account by the factors. However, this method also is affected by factor indeterminacy, which may cause substantially different factor interpretations to be obtained from the same original data. This weakness is particularly a problem in exploratory analysis where the factor structures are determined by the data set (Velicer and Jackson 1990). In this study, the solutions found through principal axis factoring are similar in form to those found by principal component analysis, thus factor indeterminacy is not likely to be important. Since principal axis factoring generally provides more interpretable solutions, it was chosen as the extraction method.

The two methods of factor rotation investigated in this study are orthogonal and oblique rotation. Rotation is used to reorient the factor loadings so that the factors are more interpretable. Orthogonal rotation assumes that the factors are at right angles to each other; in other words, the factors are not correlated. For example, if the factor loadings from a set of variables are plotted on a two dimensional set of axes, the variables that load on one factor would lie along one axis, and the variables that load on the other factor would lie along the other. The VARIMAX rotation option in SPSS/PC+, which tries to minimize the number of variables that load highly on a factor, uses the orthogonal assumption. Oblique rotation relaxes the assumption that the factors must be orthogonal. In this method, one set of variables may lie along an axis, while the other set may lie along a 45 degree angle to the axes. Allowing for correlations between the factors often simplifies the factor solution since many attitudinal dimensions are, in fact, likely to be correlated. SPSS/PC+'s OBLIMIN procedure uses oblique rotation (Norusis 1990b). (Note: Unlike orthogonal rotation, the pattern matrix and the structure matrix are not equal after oblique rotation. However, only the pattern matrix need be examined since it allows for the easiest interpretation of factors (Rummel 1970)). The pattern matrices found using oblique rotation are more interpretable than the orthogonal rotation solutions, with fewer variables loading significantly on more than one factor. Thus, the oblique rotation method is used in the final factor analyses.

The final decision to be made when conducting factor analysis is to determine the number of factors. One rule of thumb is to use an eigenvalue of one as the cut-off value. That is, all factors in a particular solution must have eigenvalues greater than one. Also, one can look at the scree on a plot of eigenvalues against the number of factors. The point at which the eigenvalues begin to level off can also be used as a cut-off point (Velicer and Jackson 1990). However, perhaps the best method in an exploratory approach is to use the eigenvalue and scree cut-off points as general guides to the dimensionality of the factor space and let the interpretability of the factors indicate the exact number of factors to retain. For example, if a solution has a factor with an eigenvalue close to one but one or more factors do not have an obvious meaning, then the solution may be reasonably discarded. In the factor analyses conducted in this research, the eigenvalue cut-off of one was used in choosing four factors for the job satisfaction variables. But, for the work characteristics variables, a solution in which one of the six factors had an eigenvalue slightly greater than one was excluded since it had a uninterpretable factor (only one variable had a significant factor loading). Instead, the five factor solution was chosen.

4.3 Part B Factors: Job Satisfaction

The factor analysis procedure produced four factors that explain 51.0% of the variation in the job satisfaction questions. Table 4-1 shows for each variable the factor loadings that are greater than 0.25. The negative loadings are caused by questions that are negatively oriented to the factor, thus ineffective supervisor communication (NSUPCOMM) has a negative loading on the supervisor factor. Both positively and negatively oriented questions were used in the survey to minimize an automatic response bias by the respondents. The correlation between the supervisor and frustration factor is 0.45 and between the satisfaction and frustration factor is 0.34. All other factor correlations are less than 0.3. The presence of frustration factor in the high correlations is not surprising since this factor has the lowest loadings making it less well-defined compared to the other factors.

The first factor deals with the respondent's interaction with the supervisor. The self-rating of how well the respondent works with the supervisor has the highest loading. Next comes poor supervisor communications which is loaded negatively. This means that good communication (a negative attribute rating) would contribute to a positive score on this factor indicating a good relationship with the supervisor. The other important variables (not being appreciated by the supervisor, having an effective work team, and having the opportunity for promotion) also involve supervisor relations.

The second factor can be interpreted as the satisfaction with the work performed by the respondent. Here, the highest-loading variables are the overall satisfaction with work and having a sense of accomplishment. Lack of supervisor appreciation and likelihood to look for a new position have much lower loadings. An employee's satisfaction is likely to be related to the attention given by the supervisor. Finally, satisfaction with the current job is likely to be negatively associated with the desire to search for a new one.

Workplace interaction effects load on the third factor. The negative sign on the loading for not getting along with co-workers means that getting along well with co- workers (i.e., a strongly negative attribute rating) will contribute to a high positive score on this factor. The other variable, confidence in the ability to do the job, may also reflect interaction effects. Those who are confident in themselves often work well with others (for example, they may be less apt to blame others for their own faults, which would lead to interpersonal conflicts).

The final factor has been interpreted as the frustration the respondent feels toward the job. The most important loading is for the variable on the likelihood of looking for a new job, which can be associated with job frustration. Also loading on this factor, the belief that the job is tedious and boring reflects feelings of disappointment with the position. Finally, the lack of resources to complete assigned tasks can also be associated with frustration on the part of the respondent.

Just as the means were calculated for each separate question in part B (see section 3.4), the mean factor scores can also be computed (see Table 4-2). The mean scores on each factor across the sample will be zero because factor scores are standardized during the factor analysis process. Thus, the values presented in Table 4-2 can be interpreted as the number of standard deviations (where the standard deviation is calculated on the entire sample) from the overall sample mean. Overall, home-based telecommuters rate their supervisors more highly than the other groups. Prospective telecenter users are the most satisfied with their position, and home-based telecommuters are the next most satisfied. Social and professional interaction effects are highest for the non-telecommuters and lowest for the center users-to-be. Finally, non-telecommuters are more frustrated with their job than the other two groups. An analysis of variance was conducted on the means for each factor; however, no significant differences between study groups were found using a level of confidence of 0.1. The small sample size of the control groups may have affected the outcome of the analysis of variance.

4.4 Part C Factors: Work Attitudes

The first factor includes many of the direct benefits to the employee at the workplace. The most important variable here is the respondent's desire to dress how s/he likes. The next two variables with negative loadings indicate the benefits of a workplace free from distractions and with a hassle-free commute. Other important benefits to the respondent are protecting the environment and having control over the condition of the workplace. Also, cost savings and stress at the workplace are associated with this factor. The remaining significant loading variables, the workplace would have a professional appearance and opportunity for social interaction (both loading negatively), each load more strongly on other factors, and their association with the personal benefits factor, although of the expected sign, is weak.

The second factor can be interpreted as the respondent's work ethic, that is, the desire to work effectively and competently. The loadings on professional appearance, working effectively, and being motivated translate into a strong work ethic. The ability to keep home and work activities separate and minimize household conflicts are also significant to this factor. Both frustration over not having necessary equipment and fear of indulging in unhealthy activities also point to a strong belief in working hard. Not surprisingly, one who wishes to work hard wants to have a less stressful workplace and be free of distractions. For the second lowest loading, lack of free time is associated with a strong work ethic which may mean that those who work hard do not have extra time. And finally, having enough opportunity to interact socially with co-workers is related to this factor; however, those with a strong work ethic are likely to be satisfied in this regard since a choice to concentrate on work activities may also mean a choice to minimize social interaction.

Work responsibility, the third factor, has the fewest number of significantly loading variables. Responsibility is shown here by the desire to have work judged by the results rather than the presence of the employee at the work site. In addition, respondents include the need for independence in daily activities and the freedom to schedule work tasks as variables that describe this factor. Having control over the work environment also expresses responsibility for work activities. The final and weakest-loading variable, the ability to run errands, does relate to responsibility; however, here the issue is most likely taking care of household, rather than work, responsibilities.

The family drive is present in the fourth factor. The ability to handle dependent care has the highest loading. Having free time, the next highest loading, is an important component for family life. Also, balancing work and home activities and working while sick or disabled are important to the well-being of the household. The ability to run errands on the way to and from work can be important to the family: for example, the errand may be picking up a child from school. Other loadings include the desire to have an easy commute, which can prevent the transfer of work stress to the home, and benefitting the environment, so that family members are not adversely affected by the respondent's actions. Financial concerns, which also have lower loadings, can be especially important in household interactions.

The final factor, which involves concerns the respondent may have about the supervisor and vice versa, is similar to the job satisfaction factor about the supervisor but oriented in the opposite (negative) direction. The strongest-loading variable is difficulty with supervisor-employee communication. Next in importance is the concern of not being visible to the management, which can affect promotion opportunities. The need for self- discipline is likely included here because if the employee does not have self-discipline, then the supervisor is needed to give it. This factor also incorporates the need for professional and social interaction at work, both of which often involve the supervisor, and may reflect, at least in part, the supervisor's ability to provide a supportive work environment. Not surprisingly, supervisor discomfort with the work location is also included in this factor. Although the variable accounting for the need for enough space to work may appear to be out of place in this factor, its loading may reflect a concern on the part of the supervisor, or the perception of the respondent that there is such a concern.

Since the work attitudes factors were calculated from variables for all three workplaces, each work attitudes factor will have, in general, a non-zero mean for each workplace even though the overall mean for all workplaces is zero (see Table 4-4). Based on the attitudes of all respondents, the telecommuting center is seen as a midway point between the regular workplace and home for most of the factors. The personal benefits of the work arrangement are strongest from home, but still important from the telecenter. The center is seen as an effective workplace for completing work tasks, while home is perceived to be the least effective work environment. On average, working from home requires the most work responsibility, working from the office requires the least, and working from the telecenter requires only average responsibility. Although family responsibilities are best handled by working at home, working at the center also provides opportunities for handling family care. Similarly to the third factor, supervisor concerns are high from home, average from the center, and low for the regular workplace. As a result, telecommuting from a center seems to mitigate some of the impacts, both positive (personal benefits, family care) and negative (supervisor concerns), of telecommuting from home.

The factor means for each study group at each workplace are also reported in Table 4-4. Although the overall mean for personal benefits was highest at home, the prospective telecommuting center users rated the personal benefits at the center slightly higher than for home. For the work ethic factor, each study group rated its workplace location as the best place to get work done. The group means for the other three factors mirror the rankings of the means for all groups combined. Unlike the job satisfaction factors, the work attitudes factors have significantly different means among groups and workplaces as shown by the p-values from a two-way analysis of variance (see Table 4-5). All workplace main and interaction effects are significant (shown in boldface type) for the five factors at a level of confidence of 0.1. Only two factors are not significant for the study groups: work ethic and work responsibility. For these factors, the means are not significantly different for the center-based, home-based, and non-telecommuters.

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