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Consumer unit types and expenditures on food away from home.

For a long time marketers and other social scientists have been interested in the relationship between household or family type and buyer behavior. At the applied level, companies like the McDonald's Corporation have used family type as a segmentation variable, and a substantial portion of television and print advertising is structured around explicit differentiations. In an effort to predict and explain variations in behavior among different types of families, family life cycle (FLC) theory was developed as an alternative to age and other single-variable segmentation schemes (Lansing and Kish 1957). Since then, various additions, explanations, and applications of FLC have appeared in the literature (e.g., Fodness 1992; Murphy and Staples 1979; Stampfl 1978; Wagner and Hanna 1983; Wells and Gubar 1966).

Though not often operationalized in this way, FLC is basically a process theory. Families go through different stages from formation through development and reorganization and eventually disintegration as spouses die. Each stage purportedly is linked to different patterns of purchasing (Derrick and Lehfeld 1980; Wagner and Hanna 1983). When the issue of market segmentation is addressed, it is done in a cross-sectional manner; that is, each family type is considered to be a unique segment and the notion of process is not considered. FLC theory has been criticized for failing to account for differences in socioeconomic and other demographic factors (Pol and Rader 1986; Wagner and Hanna 1983). Specific criticisms regarding the lack of control for income (Ferber 1979) and the exclusion of nontraditional families (Derrick and Lehfeld 1980) also have appeared.

Consumer researchers can make good use of the portion of the FLC theory that focuses on differential buyer behaviors across variations in family types. For segmentation and targeting purposes, measuring the differences in what may be considered the propensity to purchase products and services across consumer unit types is of substantial value in evaluating the market potential of a particular segment as well as in developing segmentation and targeting strategies.(1)

This paper focuses on the use of consumer unit types to segment the food-away-from-home market. Initially, eight consumer unit segments are identified and comparisons in per capita purchasing are made. Income and race/ethnicity are used as composition variables; that is, factors that are considered to be important in food-away-from-home expenditures, and, therefore, hypothesized to modify the initially observed relationship between food-away-from-home expenditures and consumer unit types. A major objective of this study is to show how an analytic method referred to as log-linear purging can be used to control for the effects of income and race/ethnicity on expenditure patterns across different types of consumer units. The results of log-linear purging analysis reveal the composition-controlled propensity to purchase food away from home for each consumer unit segment. Propensities are presented in percentage terms which provide consumer researchers with simple and straightforward information that can be subsequently used in making strategic decisions.


The restaurant industry is undergoing significant change in the United States. Although 1994 sales are projected to be $275 billion (4.3 percent of GDP), the industry is experiencing difficulties (Carlino 1994). Seemingly, shifting cultural preferences regarding the value placed upon time spent at home along with economic restructuring have brought about a stagnation in expenditures on food away from home. While the average amount of money spent by households on food was basically constant from 1989 to 1991 ($4,300), the amount spent on food away from home dropped nearly $150 to $1,600 over the three-year period (U.S. Department of Labor 1993). As a result, all food expenditures classified as away from home decreased from 42.4 to 37.9 percent of the total spent on food.

As the major component of this trend, the restaurant industry has shown slow growth since the late 1980s. According to a CREST (Consumer Reports on Eating Share Trends) report, between 1989 and 1990, total industry sales increased a mere 1.7 percent, the third year of very slow growth. Sales for lunch, the most popular meal away from home, increased only 0.7 percent from 1990 to 1991 (Ryan, Stephenson, and Strauss 1992). The growth rate of store units for the top 100 chains was only six percent for the 1988-1989 fiscal year. Industry giant McDonald's has experienced a U.S. revenue stagnation in the last five years with increased profits mainly due to cost cutting efforts (Berss 1993). The company has turned to the international market as its major source of growth (Willis 1993).

The reasons for the shift away from dollars spent on food away from home have yet to be clearly understood. Demographic change would lead industry analysts to expect increases in food-away-from-home expenditures. The percentage of all adult women who are in the labor force, particularly those women who have young children, continues to increase, placing a greater premium on time. The working environment has become less predictable, with longer work weeks and greater diversity in hours worked. More, and a larger percentage of, families are considered nontraditional (e.g., without children or with children from multiple marriages) than ever before. Between 1980 and 1992, husband-wife families declined from 61 to 55 percent of all families. During the same period, single-parent families increased from 10.4 to 14.2 million. And nearly 24 million Americans now live alone (U.S. Bureau of the Census 1993, Table 63). All of these factors have created an environment that should foster the demand for food purchased away from home.

At the same time, sociologists and marketers have been predicting a greater degree of what has been labeled cocooning for the 1990s (Drucker 1992; Hall 1989; Rose 1990). Cocooning refers to families and other households spending more time at home. While pressures to purchase and consume prepared food have increased, a substantial portion of the population is becoming weary of a constant out-of-home lifestyle. Households are consuming more food at home at the same time they are spending more time at home. Furthermore, consumers are becoming more health conscious in regard to food consumption. Many restaurants have had a long history of offering high-fat, high-calorie, high-cholesterol, and high-sodium food items. Overall, at least in the short term, cocooning and other trends seem to have more than offset an increasingly positive demographic environment with respect to purchasing food away from home.

The current study is intended to address the stagnation in domestic revenues observed in many sectors of the food-away-from-home market. That is, to what extent does consumer unit type, income, and race/ethnicity variations account for differences in the amount of money spent on food away from home? This information should provide insight into why the fast food industry is encountering a stagnation in domestic sales and give guidance to other sectors selling food away from home. Moreover, the analyses performed should provide direction with respect to segments of the market that show the greatest potential for growth.


Expenditure data for food away from home come from the interview component of the 1989 Consumer Expenditure Survey (CE) conducted by the Bureau of Labor Statistics. The CE provides a continuous and comprehensive flow of data on the buying habits of American consumers for use in a variety of economic and marketing studies (e.g., Derrick and Lehfeld 1980; McCracken and Brandt 1987; Rubin, Riney, and Molana 1990; Soberon-Ferrer and Dardis 1991). The CE has been used to explore a range of expenditures, such as those on food, clothing, health care, insurance, and vehicles. These measurements provide support for revisions of the Consumer Price Index (CPI) by determining the weights of items in the CPI.

Surveyed consumer units for the CE comprise a national probability sample representative of the U.S. civilian noninstitutionalized population. A consumer unit is somewhat different from a household and includes (1) persons related by blood, marriage, adoption, or other legal arrangements who live in the same household (family definition), (2) persons living alone or who share a household but are financially independent, or (3) two or more persons who live together and pool their financial resources (U.S. Department of Labor 1993, 236). Until 1980, the CE was conducted at roughly ten-year intervals; now the survey is continuous. Each consumer unit is included in the sample for five quarters, then replaced. During the first quarter data are collected on demographic and family characteristics and an inventory of major durable goods is taken. Data from the first quarter are used for bounding purposes only. In the subsequent four quarters the full range of buying information is collected. Each quarter there are approximately 5,000 consumer units in the sample, and annually about 20,000 consumer units are interviewed. A consumer unit may be added to the sample in any quarter during the year.

The present analysis utilizes microdata from the third quarter of 1989.(2) Data for the 1989 CE are available on CD-ROM. The third quarter is selected because it contains the summer and fall months and therefore represents seasonal ranges in purchase variation. Annualized data are not used because one-fifth of the panel is new each quarter while one-fifth drops out. Therefore, relatively few consumer units, approximately 25 percent, have complete data (all four quarters) for an entire calendar year, and this subsample is not representative of all consumer units. Data for 1989 are utilized because the most recent CE data show even sharper declines in food-away-from-home expenditures than those seen in the early 1990s (U.S. Department of Labor 1993, 2), and it is not at all clear that these latest declines will be sustained for a long period of time. Therefore, it is logical to return to the year just prior to the period when the initial decline started, 1989. While data from the post-1989 period must be studied in the future, they do not serve as the data source for this study.

At issue is to first determine whether there are differences in spending on food away from home for different consumer unit types. The CE categorizes food expenditures into amounts spent at home and away from home. Food away from home refers to the total expenditures for all meals at restaurants, carryouts, and vending machines, including tips, plus meals as pay, catered affairs such as weddings, and meals away from home on trips. Take-out-to-eat foods (TOTE), that is, those foods purchased outside the home, but eaten at home are included (Senauer, Asp, and Kinsey 1991, 9). Meals prepared at home and eaten outside the home (e.g., school lunches) are not included. Because consumer units vary in size, the data on the amount of money spent on food away from home are converted into per capita figures. The per capita figures are then trichotomized: zero dollars spent, below the per capita median, and above the per capita median. The most important reason for converting per capita spending into discrete categories is to obtain summary rates (percentages) of purchase across groups which, in turn, are easy to interpret. The purging method utilized to analyze these data produces information on the percentages of each consumer unit type that is zero spending, below median spending, and above median spending when the effects of income or race/ethnicity are controlled. As explained in the methodology section, effect estimates, such as those obtained in a regression equation, are not needed. The per capita median expenditure for food away from home was $58.17 for the third quarter of 1989.

Per capita measures for food consumption have a long history of use (Senauer, Asp, and Kinsey 1991, 178). Utilizing a per capita figure allows for the control of consumer unit size. Equivalence scales (Deaton and Muellbauer 1980, 191-206) could have been employed to differentially weight the impact of various members of the consumer unit on food-away-from-home expenditures. However, these scales have been developed combining all food categories and do not distinguish food-at-home from food-away-from-home expenditures. Clearly, more work is needed regarding equivalency estimates for food-away-from-home purchase, although that work is not advanced in this paper. Finally, although it is somewhat arbitrary to use the median as the distinction between the low and high expenditure categories, it must be emphasized again that a continuous measure is being changed to a categorical one because a different method will be utilized to drive the decision-making process. Future studies using more recent CE data can take note of this figure (the median for 1989) and determine whether it has risen or fallen (adjusted for changes in food prices).

There are eight consumer unit types used in the analysis: husband-wife only; husband-wife, oldest child less than six years; husband-wife, oldest child age 6-17; husband-wife, oldest child 18 or older; husband-wife, other relatives; single parents, at least one child under age 18; single person; and other household. Parent-child consumer units are subdivided by oldest child age categories because there are substantial differences in food-away-from-home expenditures across the various categories (U.S. Department of Labor 1993, 67). A potential shortcoming in this categorization is that children in the single-parent consumer units are only classified as under age 18 and age 18 and over, and other consumer units are divided into only two categories: single person and other household. The consumer unit types utilized mirror most of the stages seen in family life cycle theory. Moreover, the other and single-parent units encompass recent changes in living arrangements.

Income is selected as a factor in determining food-away-from-home expenditures because previous and present CE data show that as consumer unit income rises the percentage of dollars spent on food away from home (as a percentage of all food dollars) increases. Moreover, income can be viewed more broadly as a measure of socio-economic status and thus is a proxy for education and occupation. Income data are divided into four categories: $0-9,999, $10,000-19,999, $20,000-39,999, and $40,000 and over. Race/ethnicity, operationalized as white (non-Hispanic), African-American (non-Hispanic), and Hispanic (non-African-American), is the other compositional variable. Previous studies have shown race and ethnicity to be important determinants of spending on food away from home (Soberon-Ferrer and Dardis 1991; Wagner and Soberon-Ferrer 1990). Moreover, African-Americans and Hispanics currently comprise 21.6 percent of the U.S. population (U.S. Bureau of the Census 1993, Table 24) and because these populations are growing faster than the white (non-Hispanic) population, their proportional representation will increase in the future.


Standardization and Log-Linear Models

The preliminary analysis of the third quarter 1989 CE places 14, 43, and 43 percent of consumer units into the non, low, and high expenditure categories, respectively. The initial percentages in the non, low, and high expenditure categories for each consumer unit type are analogous to crude rates because they do not account for the effects of composition (Halli and Rao 1992, 7-9). Demographers have long recognized the value of controlling for compositional effects when making rate comparisons (Halli and Rao 1992, 7-9). Traditionally, demographers controlled compositional effects through standardization. The standardization procedure may be considered a "what-if" process. For example, how do consumer unit-specific crude rates change if the income distribution of each type is the same? Basically, standardization produces an estimate of the percentage of consumer units in each food-away-from-home category assuming that the income composition for each consumer unit type is the same. By making the income composition of each type identical, the resulting rates (percentages) can be compared across the types without concern for the compositional effects. The effects of race/ethnicity can be controlled in the same manner. Standardization has been used to assess the market potential of areas with different demographic compositions (Pol and Tymkiw 1991). However, consumer researchers who use demographic data extensively rarely incorporate percentage adjusting procedures to compare groups or populations.

Standardization, nevertheless, has its limitations. Little and Pullum (1979) have shown that standardization is an appropriate method of calculating summary rates only when there are no high-order interactions among composition, group, and dependent variables. Fleiss (1981) argues that if rates vary in different ways across the composition variables, then no single method of standardization will indicate that these differences exist.

To overcome the limitations mentioned, a different procedure was developed (Clogg 1978; Clogg, Shockey, and Eliason 1990). This procedure, the purging method, is based on the multiplicative or log-linear model for contingency tables. Many consumer research questions can be expressed in terms of cross-classifications of composition, group, and dependent variables. In this study, the composition variables are income and race/ethnicity, the group variable is consumer unit type, and the dependent variable is quarterly per capita expenditures on food away from home, trichotomized as discussed. The main question is to what extent do consumer units differ in per capita spending on food away from home when income or race/ethnicity differences are controlled?

Purpose of Purging

The main reason for utilizing the purging method is to calculate a summary rate (percentage) of a dependent variable for each category of a group variable excluding the influence of compositional variables. Investigating the size of the effect and its significance of an independent variable (group variable) on the dependent variable is not our concern. In this study, consumer unit type-specific percentages for per capita expenditures on food-away-from-home categories when the effect of income or race/ethnicity is controlled are calculated.

There are different approaches to studying the relationship between a group variable and a dependent variable. Logit analysis, including multinomial logit, or regression analysis with dummy coding when there is a continuous dependent variable, estimates the effect size of an independent variable on a dependent variable. It may be important to know the difference in per capita spending on food away from home between two consumer unit types, and using regression with dummy coding generates the needed information. However, the most important and straightforward information for researchers should be the summary percentages of the dependent variable for each category of the group variable because for the purpose of segmenting, targeting, and evaluating the size of a market the summary rates are more useful than the effect size. Percentages provide more concrete information upon which actions can be based than the more abstract effect estimates which must be transformed into other information before they are useful.

Crude percentages present information on the relationship between a group variable and a dependent variable, which could be confounded by compositional variables. Purged percentages expose the relationship between the group and dependent variables when the effect of compositional variables is controlled. The issue of which and how many compositional variables should be used is not crucial for the purging method because it does not require proper model specification in the sense of a regression analysis. If only the effect of income is purged, income-controlled propensities to consume (purged percentages) for each consumer unit type are obtained. By comparing the purged percentages to the crude percentages, the effect of income on purchase behavior is better understood. If income and race/ethnicity are purged simultaneously (using an income-race/ethnicity combination), an income-race/ethnicity-controlled propensity to consume can be studied.

Investigating the difference between crude rates and purged percentages provides information on which groups are sensitive, and in what direction, to the presence of compositional variables. For example, the Single (one-person) consumer units are very sensitive to both income and race/ethnicity controls, but in different directions. When income is controlled, substantially more Singles are in the high spending category compared to the crude rates. However, if race/ethnicity is controlled, far fewer Singles are in high spending category when compared to crude rates. In this study, the effect of two compositional variables, income and race/ethnicity, was purged separately, not simultaneously. The results of simultaneous control are not presented because joint control severely hampers the ability to interpret the independent impact of each composition variable. In the current study, joint control masks the individual effects. This is because the individual effects produced are in opposite directions with the joint impact being negligible. Moreover, as discussed in the analysis section, independent effects are needed because of the differences in the interpretation of the individual impact of each variable.


A general multiplicative model for the three-way table (Goodman 1978) is

[Mathematical Expression Omitted]

where [F.sub.ijk] is the expected frequency in cell (i, j, k) of a three-way cross-classification, C x G x D. C is a composition variable with I categories, G is a group variable with J categories, and D is a dependent variable with K categories. The quantity [Eta] is the overall effect and is the geometric mean of all cell frequencies. The quantity [Mathematical Expression Omitted] is the main effect of the level j of the group variable on the expected frequency [F.sub.ijk] in cell (i, j, k) of a three-way cross-classification.

The situation in which [Mathematical Expression Omitted] for at least some i, j, and k can be interpreted as claiming that group differences (consumer unit types) in levels of the dependent variable (per capita spending) vary across levels of the composition variables (income and race/ethnicity). When [Mathematical Expression Omitted] for all i, j, and k, there is no three-way interaction, the two-factor taus ([Tau]), represent the partial association between two variables controlling for levels of the third variable. Therefore, [Mathematical Expression Omitted] measures the partial association between composition and group, [Mathematical Expression Omitted] represents the partial association between group and dependent variables, and [Mathematical Expression Omitted] measures the partial association between composition and dependent variables. To make the explanation simple, we assume that [Mathematical Expression Omitted]; that is, there is no three-way interaction among composition, group, and dependent variables. The problems related to the presence of a three-way interaction are discussed later.

Using a general multiplicative model, the crude rates of category k of the dependent variable for the group j are expressed in equation (2).

[Mathematical Expression Omitted]

Substituting the right hand side of equation (1) for equation (2), crude rates, [r.sub..j(k)], can be expressed using main effects and those effects of two-way interactions as in equation (3). Notice all two-way interactions have an effect on the crude rates. Moreover, the CG interaction appears in the resulting expression of the crude rate. In other words, group differences in composition as measured by the CG interaction confound the interpretation of crude rates.

[Mathematical Expression Omitted]

The crude rate expressed in (3) explicitly shows the nature of compositional effect. From this specification of compositional effects, Clogg (1978) and Clogg and Eliason (1988) proposed calculating summary rates from frequencies that have been purged of the partial CG interaction. The partial CG purged frequencies, [Mathematical Expression Omitted], can be obtained by dividing the expected frequency of each cell, [F.sub.ijk], by the effect of CG interaction, [Mathematical Expression Omitted], as shown in equation (4).

[Mathematical Expression Omitted]

The summary rates calculated from these partial CG purged frequencies, [Mathematical Expression Omitted], are given in equation (5).

[Mathematical Expression Omitted]

Equation (5) shows that the CG purged summary rates are indeed free of the effect of CG interaction. Equation (5), however, also shows that the partial CG purged rates are not completely free of the effect of the compositional variables. The [Mathematical Expression Omitted] parameters continue to influence the summary rates through the [Mathematical Expression Omitted] parameters. The presence of [Mathematical Expression Omitted] and [Mathematical Expression Omitted] parameters in the summary rates means that the partial CG purged rates vary if marginal distributions of the composition variables vary.

To eliminate the effects of [Mathematical Expression Omitted] and [Mathematical Expression Omitted], Xie (1989) introduced partial CD purging. It produces the partial CD purged frequencies seen in equation (6):

[Mathematical Expression Omitted].

The summary rates calculated from the partial CD purged frequencies can be expressed using only [Mathematical Expression Omitted] and [Mathematical Expression Omitted] parameters as in equation (7).

[Mathematical Expression Omitted]

As the partial CD purged rates are free of all parameters involving the composition variables, Santi (1989) concluded that partial CD purging may be viewed as an improvement over partial CG purging.

Partial CG purging and partial CD purging have been performed based on the assumption that there is no three-way interaction among composition, group, and dependent variables. In this case, the three-way interaction means that group differences in the dependent measure vary at different levels of the composition variable. Fleiss (1981) and Little and Pullum (1979) have cautioned against using standardization when the three-way interaction exists.

Clogg, Shockey, and Eliason (1990) introduced a way to purge the effects of three-way interaction. This is called partial CG and CGD purging. Although it is possible to purge in such a manner, it should be noted that the summary rates calculated from the partial CG and CGD purged frequencies must be in agreement before they can be used. Clogg, Shockey, and Eliason (1990) acknowledge that if the summary rates are calculated in the presence of three-way interaction, information is lost. Their interest is in determining how much information is lost by comparing the summary rates calculated from the partial CG purging and the partial CG and CGD purging.

Is Purging Necessary?

Purging of income

Table 1 clearly shows that the level of income and per capita spending on food away from home are closely related. The range for consumer units in the non category, no money spent on food consumed away from home, is from 31.2 percent for families with incomes less [TABULAR DATA FOR TABLE 1 OMITTED] [TABULAR DATA FOR TABLE 2 OMITTED] than $10,000 to 2.8 percent for consumer units with incomes over $39,999. A similar observation can be made about the high spending category; there is an increase from 24.3 percent for the lowest income level to 59.9 percent for the highest level.

While Table 1 shows that income and per capita spending on food away from home are strongly related, Table 2 indicates that different consumer unit types have very different income distributions. For example, 9.4 percent of Husband-Wife only consumer units have incomes less than $10,000 and 35.2 percent of this consumer unit type have incomes of $40,000 or more. While 39.2 percent of Singles have incomes less than $10,000, only 8.9 percent of this consumer unit type have incomes of $40,000 or more.

The crude rates of spending within consumer unit types vary considerably. For example, the crude rates (proportions) for no, low, and high spending for Singles are .1904, .2693, and .5403, respectively, and the crude rates of no, low, and high spending for Husband-Wife with own children older than age 17 (HW c [greater than] 17) consumer units are .0740, .4986, and .4274, respectively (data from Table 7). The concern is how to compare these rates when the following information is known: a large proportion of Singles have low incomes, and a large proportion of HW c [greater than] 17 have high incomes. Moreover, the level of income and per capita spending on food away from home are closely related. In order to fully understand which consumer unit type is the most sensitive to the effect of income, the crude rates and income-controlled rates should be compared. Purging provides the mechanism for this control and comparison.

Purging of race/ethnicity

Table 3 clearly shows that race/ethnicity and per capita spending on food away from home are closely related. While 11.5 percent of the white consumer units did not spend any money on food away from home in the third quarter of 1989, 32.9 percent of African-American and 24.7 percent of the Hispanic consumer units are in the no spending category. The high spending category also shows differences across race/ethnicity categories from 46.5 percent for whites to 23.3 percent for Hispanics.

Table 4 indicates that there are very different racial/ethnic distributions across consumer unit types. For example 92.7 percent of Husband-Wife only consumer units are white, while only 3.2 percent of this consumer unit type are Hispanic. However, the consumer unit Single Parents with children younger than 18 years old exhibits a very different distribution. That is, 59.6 percent of this consumer unit type are white and 11.4 percent are Hispanic. Purging of race/ethnicity effects is clearly required in order to better understand per capita spending/consumer unit type relationships.

Distributions of Per Capita Spending for Racial/Ethnic Categories

Food Away From Home Per White African-
Capital Spending (quarterly) Non-Hispanic American Hispanic

Consumer Units (number) 4,123 520 296

No ($0) (%) 11.5 32.9 24.7
Low ([less than] $58.17) (%) 42.0 42.3 42.0
Low ([greater than] $58.17) (%) 46.5 24.8 23.3



Tests for Three-Way Interactions

Before adjusting any rates using the purging method, we must ensure that there are no three-way interactions. Therefore, the first step in the analysis is the examination of log-linear models for a three-way table. The results determine whether and how to calculate adjusted summary rates (Clogg and Eliason 1988). The models using income as a compositional variable in Table 5 and race/ethnicity in Table 6 were tested using log-linear routines available in SPSSX.

Log-Linear Models for Three-Way Table, Income (C) by Consumer Unit
Type (G) by Per Capita Spending (D)

Model Margin Fitted df [L.sup.2] p

1 {C} {G} {D} 129 2,391.35 .00
2 {C} {GD} 115 2,032.15 .00
3 {G} {CD} 119 1,830.21 .00
4 {D} {CG} 94 1,146.63 .00
5 {CD} {GD} 105 1,471.01 .00
6 {CD} {CG} 84 585.49 .00
7 {GD} {CG} 80 781.43 .00
8 {CD} {CG} {GD} 70 89.22 .06

Log-Linear Models for Three-Way Table, Race/Ethnicity (C) by
Consumer Unit Type (G) by Per Capita Spending (D)

Model Margin Fitted df [L.sup.2] p

1 {G} {D} 60 927.71 .000
2 {C} {GD} 46 547.11 .000
3 {G} {CD} 56 698.08 .000
4 {D} {CG} 46 599.41 .000
5 {CD} {GD} 42 317.48 .000
6 {CD} {CG} 42 309.78 .000
7 {GD} {CG} 32 218.81 .000
8 {CD} {CG} {GD} 28 34.49 .185

Model 1 in Table 5 tests the hypothesis of mutual independence among composition, group, and dependent variables. The large likelihood ratio statistic relative to the degrees of freedom indicates this model does not fit. By comparing model 1 with models 2, 3, and 4, we can determine whether or not there are significant bivariate associations between group and dependent variables, composition and dependent variables, and composition and group variables, respectively. Each of the three comparisons shows a considerable decrease in [L.sup.2], which indicates each association is significant.

Model 4, {D} {CG}, allows for the interaction between composition and group variables and no other two-way interactions. By comparing model 4 with models 6 and 7, we can determine if there are significant interactions between group and dependent variables (model 6) and between composition and dependent variables (model 7). Each of these associations is significant. However, model 8, which includes all two-way interactions and no three-way interaction, best fits the data (p = .06). This model is selected for further use. Table 6 shows models using race/ethnicity as a compositional variable. Model 8, with all two-way interactions but no three-way interaction, clearly best fits the data (p = .185).(3) Given these p-values, the hypothesis that the model of no three-way interaction fits the data is accepted.

Once a model is selected, the use of smoothed frequencies rather than the raw cell frequencies is suggested (Clogg, Shockey, and Eliason 1990). For example, if the null hypothesis that there is no three-way interaction cannot be rejected, smoothed (expected) frequencies from the model of no three-way interaction would be generally preferable to the raw cell frequencies because (1) all smoothed frequencies will be positive while the raw frequencies may have sampling zeroes, and (2) maximum likelihood estimates of the frequencies under a restricted model will have smaller sampling variability than the raw cell frequencies when the restricted model holds. Therefore, in this study, crude summary rates are calculated using smoothed frequencies obtained from the model of no three-way interaction.

CD and CG Purged Rates

As stated earlier, two types of purging have been developed: partial CD purging and partial CG purging. Partial CD purging eliminates the effect of composition (income and/or race/ethnicity) completely. In other words, if the goal is to understand the relationships between the group and dependent variables without any effect of composition variables, partial CD purging should be used. That is, if the composition-controlled relationship between types of consumer units and spending on food away from home must be known, partial CD purged rates should be used.

On the other hand, partial CG purging eliminates only the effect of composition and group interaction. Partial CG purged rates are influenced by the effect of composition ([Mathematical Expression Omitted]) and the effect of composition and dependent variable interaction ([Mathematical Expression Omitted]). In other words, partial CG purged rates will vary if the marginal distribution of the composition variables vary. So if it is important to maintain a certain distribution of the composition variable, partial CG purging is preferred.(4)


Because the primary goal is to investigate the composition-controlled propensity to purchase food away from home across different consumer unit types, partial CD purged percentages are preferred to partial CG purged percentages. The findings focus on comparisons between crude and partial CD purged percentages. Table 7 presents the crude and partial CD purged percentages across the eight consumer unit types using income and race/ethnicity separately as compositional variables.

In this study, there are small discrepancies between the two crude percentages calculated using income and race/ethnicity as compositional variables because 13.6 percent (695 consumer units) of the [TABULAR DATA FOR TABLE 7 OMITTED] total third-quarter sample (5,103 consumer units) did not provide information about their income and 3.2 percent (164 consumer units) of the sample were classified as a racial/ethnic group other than white non-Hispanic, African-American, or Hispanic. That is, the two analyses have somewhat different sample sizes for each analysis depending on whether income or race/ethnicity is used as a compositional variable. However, as can be seen in Table 7, the crude percentages are quite similar.

Purging of Income

Several important patterns can be seen in Table 7. Overall, controlling for income results in markedly altered percentages, which indicates the income-controlled propensity to purchase food away from home is substantially different from the patterns observed in the crude percentages. Income control, in general, widens the range in percentages observed across the eight consumer unit types for all three spending categories. For example, the crude percentage for the high spending category ranges from 54 percent for Singles to 25 percent for Single Parent with at least one child younger than age 18. For purged percentages the range is from 67 percent for Singles to 17 percent for Husband-Wife other consumer units. While the rank order for crude and purged percentages is similar, the differential in percentages among ranks is far greater for the purged percentages. The highest three crude rates for the high spending category are for Singles, 54 percent; Husband-Wife only, 51 percent; and Husband-Wife with oldest child older than 17, 43 percent. The highest three purged percentages are for Singles, 67 percent; Husband-Wife only, 43 percent; and Other households, 32 percent. In addition, with the exception of the Singles category, percentages for the low spending category for purged data are higher than their crude counterparts. This indicates a greater income-controlled propensity for low expenditure for these consumer units.

More specific patterns are also seen. The income-purged percentages for the no spending category is greater than the crude percentage observations for all consumer units containing a husband and a wife. The same husband-wife consumer units also have smaller income-purged percentages for the high spending category when compared to crude percentages. Small consumer units (i.e., Husband-Wife only and Singles) have the highest income-controlled propensity to purchase food away from home. It can be argued that Singles are much less interested in staying home and have the greatest freedom to spend money on food away from home, but, as seen in Table 2, are most constrained by level of income. The other small consumer unit, Husband-Wife only, also shows a high income-controlled propensity to purchase food away from home as compared to other consumer units. This consumer unit is also characterized by greater freedom to expend money on food away from home and its high income-controlled propensity is reinforced by high income. High income-controlled propensity (43 percent) along with a high income reinforcing the propensity results in high crude percentages for the high spending category (51 percent).

For any consumer unit containing a husband and a wife, there is an underestimation (purged percentage greater than crude percentage) of no spending and overestimation (purged percentage less than crude percentage) of high spending, which can be explained by the fact that those consumer units include large numbers of high income households (Table 2). Income-purged percentages show downward adjustments of eight percent (Husband-Wife only), ten percent (Husband-Wife with the oldest child younger than six), 14 percent (Husband-Wife with the oldest child between six and 17), 17 percent (Husband-Wife with the oldest child other than 17), and 13 percent (Husband-Wife other) when focusing on the high spending category. There is also an overestimation of no spending and underestimation of high spending for Singles and Single Parents with children under 18 years of age. In particular, there is a large increase in high spending (from 54 to 67 percent) and a considerable decrease in no spending (from 19 to nine percent) for Singles. Again, income differentials account for these observations.

Purging of Race/Ethnicity

The purging of race/ethnicity shows different patterns from those of income purging. The lower panel of Table 7 indicates that the race/ethnicity-purged percentages for the no spending category are greater for all consumer unit types when compared to crude percentages and the purged percentages for the high spending category are smaller than the crude rates for all consumer unit types. This pattern can be explained by the fact that whites (non-Hispanics), which make up the major proportion of all eight consumer unit types, have the highest proportion of consumer units in the high spending category. By purging for race/ethnicity, the white effect on expenditures is removed, thus the percentages in the high category decrease while those in the low category increase.

Although the income distribution of the consumer units containing a husband and wife and those of Singles and Single Parents are quite different (inverse), the racial/ethnic distribution in each consumer unit type shows a similar pattern. As stated earlier, in all consumer unit types white non-Hispanic is the predominant segment. African-American is a larger segment than Hispanic in all consumer unit types except Husband-Wife with children younger than six and Husband-Wife with children older than 17.

The largest crude/purged differential can be found in the high expenditure category. The crude/purged percentage point differences for Husband-Wife only; Husband-Wife, child under six years of age; Husband-Wife, child over 17; and Singles are 13, ten, ten, and 12 percent, respectively. On the other hand, crude/purged percentage differences for the low expenditures category are all less than four percentage points. Finally, the crude/purged percentage point differences within the no spending category are greatest for Husband-Wife only (ten percent) and Singles (11 percent).

Table 7 also shows that income and race/ethnicity affect the percentages in opposite directions for Singles and Single Parents. The income-purged percentages for the high spending category for Singles and Single Parents are substantially greater than their crude percentage counterparts while the race/ethnicity-purged percentages for the same consumer units are substantially smaller. Therefore, if the income and race/ethnicity combination is used to purge the effects of income and race/ethnicity simultaneously, the effects of both variables cancel each other.


The analysis shows that purged percentages generate very different interpretations about expenditures on food away from home when compared to crude percentages. The crude percentages serve to distinguish general differences among the eight consumer units, and the purged percentages uncover composition-controlled propensities for food-away-from-home expenditures, which in turn can serve as the basis for marketing activities. Crude percentages, therefore, are somewhat misleading and log-linear purging offers a way to control for factors which mask the more inherent relationship between consumer unit type and food-away-from-home expenditures.

Examination of the initial rates supports the idea that the growth in nontraditional households (Singles and Single Parents) has fostered a stagnation in food-away-from-home expenditures; these consumer units have the largest crude percentages in the no spending category. However, these same groups also offer high market potential in that their crude percentages for high spending are not markedly low and their purged percentages (high category) are large compared to their crude percentage counterparts. The objective of business strategy is to move consumer units out of the no to the low or high group. Of course, a corollary strategy would be to foster an increase in spending for both the low and high categories, thus increasing the median. Income disadvantages can be overcome by price rollbacks and placing a stronger emphasis on value received. Even the cocooning trend can be incorporated in marketing efforts by stressing the drive-through or the in-store purchase/take-out-to-eat (TOTE), where food is taken home to be consumed. Grocery stores and some restaurants have increased their emphases on TOTE and some success has been noted (Hayes 1994). Hewlett-Packard Co. is testing a two-way interactive video service that, among other capabilities, allows customers to order take-out food (Leinfuss 1992). However, few efforts have attempted to link food consumption with desire to spend more time at home, a strategy that should prove successful.

In regard to race/ethnicity-oriented strategies, control for composition (majority white) increases the no spending percentage and decreases the high spending percentage. Initially, one might interpret these results as an indication that marketing efforts designed specifically to target African-Americans and Hispanics are misdirected. By holding constant the dominant effect of whites especially with respect to their representation in the high spending category, purged percentages are reduced. That is, purged percentages that are lower than crude percentages (for the high expenditure category) serve as evidence that segmentation of the market by race/ethnicity is sound strategy because the expenditure propensities for African-Americans and Hispanics are lower and marketing efforts must be designed to increase these propensities. Attempts to differentiate the market by using African-American and Hispanic individuals in television advertisements, for example, should be effective because at least some racial and ethnic minority consumer units feel alienated from the marketplace and targeting these groups should reduce their level of alienation. The use of racial and ethnic minority families in promotional efforts should provide an additional positive effect on food-away-from-home expenditures given that crude/purged percentage differences are for the most part largest for family consumer units.

The results from Table 7 also strengthen the argument that consumer unit type is a useful variable for segmenting a market. These segments are unique, relatively large, and exhibit very different expenditure patterns. Moreover, significant inter-consumer unit differentials can be found for both crude and purged percentages. Strategies must then follow that, for example, target high income-controlled propensity groups with the goal of getting them to maximize their expenditures, and/or attempt to influence the income-controlled propensities. The former strategy can be taken by adjusting business strategy to match the purchasing constraints realized by lower income households. Identifying segments with higher income-controlled propensities (crude percentage lower than purged percentage) offers insight into these segments with unrealized market potential. That is, by identifying more income sensitive segments, we have isolated those segments where there are significant opportunities to increase sales. Clearly, the analysis supports the current efforts of fast food chains to compete on the basis of price.

Competition based on price is possible because expenditures on food draw from both discretionary and nondiscretionary income. A marketing effort that demonstrates the value (social and economic) of buying food prepared away from home and eating it at home can be successful in part because expenditures on food come from monies that are both discretionary and nondiscretionary. If additional benefits can be demonstrated, discretionary income may be shifted to expenditures on food away from home. With regard to race/ethnicity, the data show a different pattern, but the strategy is similar. Racial and ethnic minority consumer units must feel that they are an important segment of the market before alienation can be reduced and sales increased. In addition to the use of racial/ethnic minority actors in promotions, attention should be paid to the types of foods, packaging, and methods of distribution; all factors which can account for cultural differences evident across these three market segments.

1 Consumer unit is used as the collective term for the eight family/household types identified for study.

2 The data utilized in the analysis were unweighted. The merits of using weighted and un-weighted data are discussed by Clogg and Eliason (1987) and Winship and Radbill (1994).

3 In a three-way contingency table, a model including the three-way interaction is the full model, which always fits the data perfectly. When the model including only two-way interactions fits the data well, this model should be selected because it is more parsimonious.

4 One application of partial CG purging is found in longitudinal studies. Suppose there are three time periods, 1970, 1980, and 1990, then the group variable is the time periods. The dependent variable is the per capita spending on food away from home. The composition variable is income. The research question concerns whether the proportion of consumer units classified as high spending on food away from home has increased over time. Because we know that spending on food away from home is affected by income, we want to make sure that in each time period a comparable income distribution is used. In this case partial CG rates are preferred to partial CD rates.


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Louis G. Pol is Peter Kiewit Distinguished Professor and Sukgoo Pak is Assistant Professor, Marketing, University of Nebraska at Omaha.

The authors thank the three anonymous reviewers for their helpful comments on an earlier draft of the paper. The authors also thank Jackie Lynch for her assistance in the preparation of this manuscript.
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Author:Pol, Louis G.; Pak, Sukgoo
Publication:Journal of Consumer Affairs
Date:Dec 22, 1995
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