Measuring
Day-to-Day Variability in

Travel Behavior Using GPS Data

**MEASURING
VARIABILITY IN TRAVEL CHARACTERISTICS**

**Framework**

Koppelman and Pas [1984], Pas [1987], and Pas and Sundar [1995] provide a framework for measuring and quantifying variability in travel characteristics. In their work, an important distinction is made between inter-personal variability and intra-personal variability. Together, these two measures of variability account for the total variability in a travel survey data set. Figure 1 shows the framework as adopted from their work.

Inter-personal variability refers to the differences in the behavior among different individuals on the same or different days. Behavioral differences among persons may be explained partially by differences in the characteristics of individuals. By incorporating such characteristics into a model, one can account for systematic differences in behavior among individuals. The portion of inter-personal variability that can be explained systematically through differences in socio-economic characteristics is referred to as explained variability. The remainder is referred to as unexplained variability.

Similarly, intra-personal variability may also be considered to have two components. The first component is called systematic day-of-week variability. This refers to the portion of intra-personal variability that may be attributed to systematic day-of-week effects. Intra-personal variability that can not be explained by day-of-week effects is random and is referred to as residual intra-personal variability.

**
Figure 1. Methodological Framework for Measuring Variability in Travel
(Source: Pas, 1987) **

Within the context of the GPS data set being used in this study, it is not possible to uniquely quantify and measure the two components of intra-personal variability. To do so, one would require several weeks of travel survey information in order to determine the systematic day-of-week component of intra-personal variability (e.g., how does one Monday differ from other Mondays?). As such, in this study, only the total intra-personal variability is measured and reported. Likewise, no models are estimated to explain differences in travel characteristics between persons (to determine explained variability) and only the total inter-personal variability is quantified.

**Methodology**

The methodological approached adopted in this study follows that presented in Pas [1987] and Pas and Sundar [1995]. The total variability in various measures of travel is split into its two components which are represented by appropriate sums of squares. In this representation, the total variability is represented by the total sum of squares (TSS), as follows:

TSS = |

(1) where

t_{ij}= number of trips made by person i on day joverall sample mean number of trips made per person per day

The total
sum of squares may be considered to be consisting of a between-person sum of
squares and a within-person sum of squares. The between-person sum of squares
is representative of the inter-personal variability while the within-person
sum of squares is representative of the intra-personal variability in the data
set. The between-person sum of squares (BPSS) is given by:

BPSS = |

(2) where

Ji = the number of days for which individual i reported travel information

mean number of trips made per day by person i

Within-person sum of squares (WPSS) is given by:

WPSS = |

(3)

Also, we have:

and

It can be readily seen that:

TSS = BPSS
+ WPSS

(4)

Therefore, the ratio WPSS/TSS provides a measure of the proportion of total variability in travel that may be attributed to within-person variability. Similarly, BPSS/TSS provides a measure of the proportion of total variability in travel that may be attributed to between-person variability. It should be noted that, even though the above formulation was provided in terms of trip frequency, the discussion and formulas can be extended in a straightforward manner to other measures of travel such as travel time, distance, etc.

**Results**

Results of the analysis of intra-personal variability for ten different travel
characteristics are provided in Figures 2 and 3. These figures show the extent
of intra-personal variability (as a percentage of the total variability in the
data set) for different sample considerations.

The 81 individuals who provided at least 3 weekdays of usable information (see Table 6) are considered for analysis of intra-personal variability. In the first type of analysis, the first 3-5 days of complete information are included. In the second type of analysis, the first 3-5 weekdays of complete information are included. Thus, a comparison between the first two types of analyses provides an indication of the impact of day-of-week effect on measures of intra-personal variability. Finally, the third type of analysis includes only three weekdays of travel information for the 81 individuals. A comparison between the second and third types of analyses provides an indication of the impact of survey duration on measures of intra-personal variability.

There are some clear messages that are provided by Figures 2 and 3. First, the degree of intra-person variability is influenced by day-of-week effects. In comparing the intra-personal variability found in the 3-5 day sample with that found in the 3-5 weekday sample, it is found that the extent of intra-personal variability reduces for virtually all travel measures. The second major finding is that the duration for which travel information is measured impacts the degree of intra-personal variability. A comparison of the 3-5 weekday sample against the 3 weekday sample shows that the extent of intra-personal variability is smaller for the 3 weekday sample. This shows that the measure of intra-personal variability increases with duration of observation.

Both of these findings are very consistent with expectations and corroborate earlier research reported in the literature [Pas, 1987; Pas and Sundar, 1995]. For example, Pas [1987] reports that, in a five-day activity data set from Reading, England, about 50 percent of the total variability in trip making may be attributed to intra-personal variability. On the other hand, Pas and Sundar [1995] find the corresponding percentage to be only 38 percent when considering a three-day sample. Thus, they too postulate that the extent of intra-personal variability increases as the duration of observation increases.

**Figure
2. Intra-personal Variability for Trip Frequencies and Travel Times**

There are two travel characteristics for which measures of intra-personal variability are directly comparable to results reported by Pas [1987] and Pas and Sundar [1995]. Pas and Sundar [1995] utilize travel survey data collected over three weekdays for a sample from the Puget Sound area in Washington. As such, their results are most comparable to the third sample considered in this study (3 weekday sample). The two measures are total trips and total travel time. With respect to total trips, the percent of total variability that is attributable to intra-personal variability for this particular sample in this analysis is about 49 percent. The corresponding percentage reported in Pas and Sundar [1995] is 38 percent. With respect to total travel time, the percent of total variability that is attributable to intra-personal variability for the 3-weekday sample in this analysis is about 52 percent. The corresponding percentage reported in Pas and Sundar [1995] is 42 percent.

In summary, it can be seen that the GPS travel data set provided measures of variability that are larger than those derived from traditional multiday travel diary data sets. In fact, the estimate of intra-personal variability found in the 3-weekday sample here (i.e., 49 percent) is very comparable to that found by Pas [1987] in a 5-day survey sample drawn from Reading, England. The estimate of intra-personal variability in total trips for the 3-5 weekday sample here is found to be 62 percent, which is considerably larger than that reported by Pas [1987]. Thus, it appears that GPS-based data collection methodologies are better able to capture day-to-day variability in travel behavior, possibly due to their ability to capture infrequent, non-regular, and rare trips that may be missed in traditional diary-based recall surveys.

**Figure
3. Intra-personal Variability for VMT and Departure/Arrival Times**

United States Department of Transportation
-** Federal Highway Administration**