Complementarity and Substitutability Among Discretionary Activities With Time-Diaries

William A. Weeks, Washington State University
U. N. Umesh, Washington State University
John K. Wong, Washington State University
ABSTRACT - Complementarity and substitutability among discretionary activities was assessed using time-diary data. Complements were more commonly observed than substitutes, particularly within a priori defined subsets of activities. The difference in results obtained using amount of time from the time-diary approach and the frequency of activity from recall questionnaires was accounted for by the method-specific factors. Demographic variables and mean activity levels had a minimal impact on the complementary and substitute relationships.
[ to cite ]:
William A. Weeks, U. N. Umesh, and John K. Wong (1987) ,"Complementarity and Substitutability Among Discretionary Activities With Time-Diaries", in NA - Advances in Consumer Research Volume 14, eds. Melanie Wallendorf and Paul Anderson, Provo, UT : Association for Consumer Research, Pages: 548-552.

Advances in Consumer Research Volume 14, 1987      Pages 548-552


William A. Weeks, Washington State University

U. N. Umesh, Washington State University

John K. Wong, Washington State University


Complementarity and substitutability among discretionary activities was assessed using time-diary data. Complements were more commonly observed than substitutes, particularly within a priori defined subsets of activities. The difference in results obtained using amount of time from the time-diary approach and the frequency of activity from recall questionnaires was accounted for by the method-specific factors. Demographic variables and mean activity levels had a minimal impact on the complementary and substitute relationships.


Individuals' allocation of time has been an important issue studied by consumer researchers. As indicated by Holbrook and Lehmann (1981), the problem with many of the studies that have emphasized leisure time activities is that they have ignored the pattern of relationships between discretionary activities. In response to this problem, the present study will examine the complementarity and substitutability between discretionary activities with time diary data.

The definition of discretionary activities for this study will be those activities that an individual is engaged in for the intrinsic value. This excludes any activity that might be associated with normal work and domestic work inside or outside of the home. To study the relationship between discretionary activities, it is first necessary to define and describe complementarity and substitutability of activities. Henderson and Quandt's (1958) definition of substitutes and complements will be used for this study. Activities will be defined as substitutes if both can satisfy the same need of the consumer. They will be considered complements if they are consumed jointly in order to satisfy a broader need. For example, one might view participation in a tennis or badminton as substitute activities. Due to a limited amount of available discretionary time, an individual may have only enough time to participate in one of these activities to satisfy a leisure need. On the other hand, a person might be involved in both conditioning exercises and football jointly, with the motivation being to improve overall physical condition for playing better football. This reflects a complementary relation between conditioning exercises and football. Complementary activities need not occur at the same time (and they probably will not). Complementarity is defined over a time period such as a week, a month, or a year.

This study will use a correlational analysis approach to measure substitutability and complementarity between discretionary activities, similar to approaches used by other researchers (Bass, Pessemier, and Tigert 1969; Hendee and Burdge 1974; Holbrook and Lehmann 1981). To be consistent with the definition in the previous paragraph, negative correlation among activities will be defined as a substitute relationship. Hence, as more time is allocated to a particular activity, less time will be spent on substitute activities. A positive correlation among activities will represent a complementary relationship, indicating that the two activities are participated in jointly to satisfy a broader need. For example, one group of individuals might go to a movie in a certain time period and may not spend any time watching television. Another group of individuals might watch television for some time, but not go to a movie. When calculated across all the subjects, the amount of time spent on television and movies will be negatively correlated and consistent with the definition of substitutes.

As previously noted, the complementarity/ substitutability relation among activities was examined by Holbrook and Lehmann (1981). One can expect, to some degree, that their findings were influenced by the sample used, the time period (1975) of data collection, and the recall questionnaire that was used. In particular, complementarity and substitutability among activities may vary based on the number of times (frequency) an individual reports being engaged in the activity (recall questionnaire), versus the number of minutes he or she indicates they spent on the activity during a given period of time (time-diary). Secondly, complementarity may vary based on the time span that is involved in assessing an individual's time allocation to discretionary activities. Activities that are substitutes over the span of one day may be complements over the span of one year. This study will attempt to explore these issues through the use of data that was collected with a time-diary as opposed to a recall questionnaire. In addition, the data having been collected in 1981 is more recent than the 1975 recall data.

In summary, the two objectives of this study are:

1) An examination of complementarity and substitutability among discretionary activities with time-diary data.

2) A comparison of the complementarity and substitutability relationship among discretionary activities that is derived from using a time diary versus a recall survey.



A national sample of 444 individuals was used for this study. The data were collected by the Institute for Social Research at the University of Michigan in 1981. The multistage probability sample was designed to represent housing units in the United States, excluding those on military installations. The sample was collected from 74 randomly selected locations and were located in 37 states and the District of Columbia. These included the New York-Northeastern New Jersey and the Chicago-Northwestern Indiana consolidated areas, the 10 largest standard metropolitan statistical areas (SMSAs) outside of the two standard consolidated areas, 32 other SMSAs, and 30 counties or county groups representing the nonmetropolitan and less urban portions of the United States.


Data collected with time-diaries for past studies have been based on a single 24-hour time period (Robinson 1977) or two 24-hour time periods (Nichols and Fox 1983). Obviously this limited sampling of time may be suspect. In order to reduce (not eliminate) this concern, the data for this study were collected over four waves (February-April 1981, May-June 1981, September-October 1981, and October-December 1981) with time-diaries. Respondents were requested to report their time allocation for 24-hour spans of time. They reported this information four times during the year The four times included two weekdays, a Saturday, and a Sunday.



The data collection started in Wave 1 with a personal interview and Waves 2-4 were conducted through telephone interviews. Based on the respondents self reports, a "synthetic week" was created. It reflects an estimate of the amount of time an individual spends on 223 activities for a period of a week (7 days). This is the same synthetic week data that Jackson-Beech and Robinson (1981) used in their study. Upon receipt of the time-diaries, the researchers coded the activities comprising time usage into one of 223 mutually exclusive and exhaustive activities, 60 of which were deemed discretionary activities and used in this study. These activities were chosen because they were similar, in some respect, to the discretionary activities selected by Holbrook and Lehmann (1981).

Sixty discretionary activities were grouped into the same a priori sets that were used by Holbrook and Lehmann (1981). These groups are presented in the Exhibit. In addition to time use, demographic information was collected (Table 1) for covariance analYsis.


For each of the 60 discretionary activities, the time in minutes was used to estimate pairwise correlation coefficients. The SAS routine was used to produce a simple correlation matrix. The correlation matrix was used as input into a Multidimensional Scaling Routine (MDS) on SAS. Metric and nonmetric versions were used to produce MDS maps.



To counter the confounding effects of demographic variables and mean activity levels on the time spent on each activity, partial correlation coefficients were estimated. A similar use of partial correlations was performed by Holbrook and Lehmann (1981). For instance, older subjects sight take more time to complete certain activities because of their infirmities. Alternatively, subjects who spend a lot of time in one type of social activity might spent a lot of time in other social activities. For instance, those with the demographic characteristics of "yuppies" might spend a disproportionately large amount of time on social activities. By holding these variables constant, unbiased measures of complementarity and substitutability are more likely to be obtained. Therefore, MDS solutions were produced using simple and partial correlation matrices as the inputs.

To further study the effect of these covariates, four types of simple and partial correlations were defined, 1) simple correlations among activities (r), 2) partial correlations controlling for mean activity level (rcm), 3) partial correlations controlling for demographic variables (rcd), and 4) partial correlations controlling for mean activity and demographic variables (rcdm).


Effect of the Covariates

The covariates that were hypothesized to have an effect on the correlation of activities are listed in Table 1. Each activity was treated as the dependent variable and was regressed with the covariates as the independent variables. A total of 60 regressions were run, one for each activity. The percentage of regressions where each covariate was significant is indicated in Table 1. Mean activity was the-most significant variable. Family income was significant more often than any of the other demographic variables. The demographic variables used here appear to have a lower impact on time spent on each activity as compared to the annual frequency of the activity (as noted by Holbrook and Lehmann 1981).

Measure of Complementarity/Substitutability

The degree of complementarity/substitutability was assessed using simple correlation r and partial correlation rcdm. The pairwise correlations were classified as either those between activities within each of the 7 groups or between activities across different groups. Only those correlation coefficients that were significant (p < .05) are listed in Table 2.

Using a simple correlation measure, complementarity (positive correlation) was a little more common within the a priori defined sets (6.6%) as among the groups (5.6%). Substitutability (negative correlation) was less often observed (.66% and .5% for within and between sets). Complements were more often observed than substitutes. The results from using partial correlations rcdm were very similar, with complementarity observed somewhat more often within sets than between sets. When a lower level of significance was used to assess complementarity, the difference between the within activity set of correlations and between activity set of correlations was even higher. A closer review of the activities revealed that T.V. watching was a substitute for many activities. When T.V. watching was removed from the list of activities for analysis, the estimated level of substitutability fell further. Thus, in comparison to results obtained with recall data by Holbrook and Lehmann (1981), the proportion of both complements and substitutes were lower with diary data. In both approaches, more complements than substitutes were observed. However, unlike in the Holbrook and Lehmann (1981) study, the degree of complementarity in this study was less influenced by membership to the a priori defined sets of activities.

The number of compliments observed is significantly more than what might be arrived at by chance. For an alpha level of 5% (used here) one might expect to see 2.5% complements and 2.5% substitutes. The percentage of complements observed is greater than this chance percentage in all categories in Table 2. The proportion of substitutes was, in general, less than 2.5%. Taking into account the chance factors, the true proportion of substitutes is probably even lower than observed. This bolsters the argument that complements were more commonly observed than substitutes.

One possible explanation comes to mind for this abundance of complement relationships. Prior to discussing this issue it would be helpful to review the definitions of substitutes and complements. Activities are substitutes if both can satisfy the same need and they are complements if they are consumed jointly in order to satisfy some particular need.

One explanation for the abundance of complement relationships is grounded in the Economic Law of Diminishing Returns. One might view consumers as maximizing their utility by indulging in a variety of activities rather than in a single activity that has diminishing returns from excessive involvement. For example, lets say a person has 10 hours a week (one hour a day Monday-Friday and 5 hours on Saturday) for participating in discretionary activities where his primary need is physical fitness. Normally, he jogs from Monday through Friday during his lunch hour for a total of five hours a week. Even though he has an opportunity to jog on Saturday he prefers to go hiking for five hours because he is relatively bored with jogging and feels he will maximize his incremental utility by hiking. This will lead an investigator to conclude these are complement activities.

The simple r and partial rcdm correlation matrices were each analyzed using metric and nonmetric MDS procedures. The Kruskal stress and the correlation between input and output data for a 2 dimensional solution are reported for all four resulting analysis in Table 3. We used both measures because they are not exactly equivalent though similar. For instance, two MDS solutions with the same Kruskal stress value may have different correlation values. Nonmetric analysis of simple correlation matrix produced the best fit and was chosen for further analysis. The input-output correlation of .501 is slightly better than that obtained by Holbrook and Lehmann (1981). The choice of 2 dimensions was decided by calculating the input-output correlation coefficients from 1 through 6 dimensions. These correlations were, (1) .413, (2) .501, (3) .562, (4) .607, (5) .648, and (6) .684 corresponding to the dimensionality of the solutions. Marginal diminishing returns and the ease of interpretability resulted in choosing a 2 dimension solution (as also done by Holbrook and Lehmann 1981 albeit with a lower correlation coefficient for two dimensions). The 2 dimensional nonmetric MDS solution using simple correlation matrix is presented in Figure 1.

After rotating the MDS output to facilitate interpretation of the results, some commonality was observed between the dimensions here and in past studies (Bishop 1970; Holbrook and Lehmann 1981; Witt 1971). A visual examination of the horizontal dimension (x) suggests the distinction between indoor-social activities on the right (theater, visiting, meals at friends, museums) and outdoor-individualistic activities on the left (fishing, walking, hiking). The vertical axis (y) has more sedentary activities at the top (books, magazines, phone) and more active pursuits at the bottom (camping, pleasure drives, skiing).



Television viewing is one activity that appears to be a substitute for almost all activities. The number of minutes spent on watching T.V. influences an individual's ability to spend time on other activities--a distinction that is not apparent from the data on frequency of television watching obtained with the recall procedure used by Holbrook and Lehmann (1981).

Most activities fit in the a priori clusters. The activities in the sets are somewhat different from those used by Holbrook and Lehmann (1981), and in some cases they are nominally similar but satisfy completely different needs. As an example, the eating activities set includes meals at friends, meals at restaurants, and picnics. One should not be surprised to find meals at friends near visiting and phone conversations, or eating at restaurants located near parties. These findings are consistent with McKechnie (1974). Likewise, discovering that a picnic falls within the outdoors activity set is noted by Witt (1971).






When using the diary method the results indicated most activities were neither complements nor substitutes. Further, complements were more plentiful than substitutes. Demographic variables and mean activity times influenced the estimates of complementarity.

The diary method produced results different from results obtained from a recall method. Bishop, Jeanrenaud, and Lawson (1975) report a good correlation between diary-based and recall-based time measures; however, comparison of the results in the current study with those of Holbrook and Lehmann (1981) indicate important differences do exist between the two procedures. First, demographic variables and mean activity times influence the correlations calculated from the two approaches differently. Part of the reason could be the systematic bias that results when subjects report on recall questionnaires. Recall information is typically obtained for the previous 12 months, and individuals may not be able to accurately remember how often they undertook an activity. Subjects with similar demographic characteristics might feel socially pressured to misreport the time spent on certain activities. Mean activity time may be positively related to certain activities within certain sets i.e., those who over-report their number of discretionary activities participated in, might systematically over-report all social activities but not other activities. With time-diaries, where activities are recorded soon after they are completed, these biases are less likely to influence reporting. Consequently, demographic variables and mean activity time that cause these biases, are less likely to be associated with activity time correlations, as observed.

The degree of complementarity using the diary method appears to be less than the degree of complementarity estimated using the recall method by Holbrook and Lehmann (1981). The difference in estimated complementarity appears to be related to the interval of observation. Many activities that are complementary for an individual over the course of a year (recall method) might be substitutes during the synthetic week. For instance, an individual is unlikely to participate in skiing and camping in a single day but over a year the individual who often skis in winter might camp frequently in the summer. Thus, the indication of fewer complementary activities observed in the diary method should not be viewed as a form of bias; rather, complementarity must be specified over a definite time period, with the time period determining the level of complementarity.

Another reason for finding fewer significant complementarity/substitutability relations with a time-diary is the higher variance associated with the time measures. As the time period of diary data is small, most activities are reported to have not been performed. The time spent on activities that are reported to have been performed far exceeds the amount of time spent on these activities in a typical week. For instance, if a typical subject spends one hour in one week of the month working in the garden, the average time spent on gardening each week is 15 minutes. Using a weekly diary, a fourth of the subjects will report spending one hour and the remaining subjects will report that they did not engage in gardening. Such reporting arbitrarily increases the variance of the estimates and consequently reduces the significance of the estimated correlation. Since complements and substitutes are defined only when significance of inter-activity correlation exceeds 95% (p < .05), fewer complements and substitutes are observed using the diary met nod.

Overall, it can be said that the two approaches, diary and recall. are alternate ways of looking at a problem with each providing its own implications. Complementarity cannot be rigidly defined, but must be viewed in the contest of the time interval. Classification of activities into rigid complement and substitute classes should give way to varying degrees of relationships that are conditioned by the needs of the researcher.


Bass, Prank M., Pessemier, Edgar A., and Tigert, Douglas J. (1969), "Complementary and Substitute Patterns of Purchasing and Use," Journal of Advertising Research, 9, 19-27.

Bishop, Doyle W. (1970), "Stability of the Factor Structure of Leisure Behavior: Analysis of Four Communities," Journal of Leisure Research, 2, 160-170.

Bishop, Doyle W. , Jeanrenaud, Claudine, and Lawson, Kenneth (1975), "Comparison of a Time Diary and Recall Questionnaire for Surveying Leisure Activities," Journal of Leisure Research, 7, 73-80.

Hendee, John C., and Burdge, Rabel J. (1974), "The Substitutability Concept: Implications for Recreational Research and Management," Journal of Leisure Research, 6, 157-162.

Henderson, James M. and Quandt, Richard E. (1958), Microeconomic Theory: A Mathematical APProach, New York: McGraw-Hill Book Co.

Holbrook, Morris B. and Lehmann, Donald R. (1981), "Allocating Discretionary Time: Complementarity Among Activities," Journal of Consumer Research, 7 (March), 395-406.

Jackson-Beech, Marilyn and Robinson, John P. (1981), "Television Nonviewers: An Indangered Species," Journal of Consumer Research, 7 (March), 356-359.

McKechnie, George F. (1974),"The Psychological Structure of Leisure: Past Behavior," Journal of Leisure Research, 6, 27-45.

Nickols, Sharon Y., and Fox, Karen D. (1983), "Buying Time and Saving Time: Strategies for Managing Household Production," Journal of Consumer Research, 10 (September), 197-208.

Robinson, John P. (1977), How Americans Use Time, New York: Praeger Publishers, Inc.

Witt, Peter A. (1971), "Factor Structure of Leisure Behavior for Sigh School Age Youth in Three Communities," Journal of Leisure Research, 3, 213-219.