Multivariate mapping for experienced users: comparing extrinsic and intrinsic maps with univariate maps

The main purpose of multivariate maps is to compare spatial distribution two or more phenomena (Slocum et al. 2010; Kraak et al. 2020). This solution enables the amount of information conveyed by a single map to be increased (Nelson 2020). It also helps users to find relationships between two or more phenomena that they are searching for or that they might not suspect are present. Multivariate maps are also a compact solution. They help to save space when designing maps: instead of preparing a series of maps, representing the same area but with different variables, a map maker may choose to produce a single multivariate map. However, multivariate maps are challenging for users due to visual complexity (Dent, Torguson & Hodler 2009; Huber et al. 2007; Nelson 2020). Furthermore, multivariate maps are not often applied in popular media; therefore, a potential user may not be familiar with this kind of solution nor experienced in using it. As a result, users may be discouraged from further analysis of the (too) complex map. As Nelson (2020) noted, a map maker must thus balance the benefits and insights enabled by multivariate maps with expectations of the audience's ability and willingness to engage with the challenging map. Although many authors elaborated on multivariate mapping, empirical evidence with an in-depth insight into user visual behavior when using multivariate maps is still needed.

The aim of the study reported here is to evaluate the consequences of applying multivariate maps using two designs. Unlike other authors (mainly evaluating bivariate map options), we compared three solutions when mapping four variables: two types of multivariate maps and a simple univariate alternative (serving as a baseline). As widely proved, design matters (e.g. Kiik, Nyström & Harrie 2017). Therefore, similar to Šašinka et al. (2019), we assumed that, depending on the form of multivariate visualisation, the resulting cognitive load will differ. We also expected the processing difficulty to be different for each of the multivariate combinations, based on selective attention theory (Nelson 2000b). Furthermore, we assumed that the task type also affects the results when using different multivariate maps. The different kinds of information (elementary or more complex) may be easier or more difficult to acquire depending on the multivariate map design and the number of variables encoded in a particular map. Due to the cognitive effort involved when decoding multivariate maps, we wanted to verify whether the effort connected with working with a single four-variate map is considerably more challenging than when working with a series of univariate maps. Furthermore, we wanted to get an insight into the studied process; we therefore decided to analyse basic eye-tracking metrics to support the analysis of the usability performance metrics.

There is a wide scope of choices of thematic map types, as well as involved graphic solutions. The options have more- or less-integrated visual variables to represent the mapped variables (Korycka-Skorupa & Nowacki 2019). The variables can be designed in a separable way, applying inter-symbol encoding (Nelson 2020; see examples on Fig. 1 left). The resulting image is an extrinsic map (Šašinka et al. 2019, 2021). A straightforward combination of two or more variables represented by distinct, separable visual variables results in inter-symbol encoding in extrinsic maps. The two variables are shown concurrently on a single map, but each of them can also be presented independently on two separate maps. The most common combination is a choropleth map with a graduated/proportional symbols map.

Figure 1

Further visual integration of the visual variables when mapping multivariate data in a more challenging solution. The two mapped phenomena are visually inseparable by applying intra-symbol encoding (Nelson 2020a); thus, an intrinsic map is achieved (Gershon 1998; Šašinka et al. 2019, 2021; see Fig. 1 right). The most commonly applied example of an intrinsic map is a bivariate choropleth map, incorporating two colour scales into one.

E.S. Nelson (2000b) considered bivariate symbols in relation to selective attention, the approach developed in psychology. The author grouped sets of visual variables into those that support selective attention and those that fail to do so. The first category is called separable design and includes size–hue (e.g. applied to proportional circles with fills according to a sequential colour scheme) (Nelson 1999, 2000a). It is considered that the category of integral design does not support selective attention and does not facilitate the extraction of specific variable information. The design is created by applying, for example, value-saturation (for bivariate choropleth maps) or rectangle height and width. Nelson (2000b) also distinguished a category of configural design, which includes setting separable halves of circles to use with the following pairs of variables: size–size.

As listed above, there is a wide scope of available design solutions when mapping many variables, but they differ in terms of cognitive load for map users. It is claimed that multivariate maps, especially with intrinsic encoding, increases the cognitive abilities needed to read the map, and makes the presentation challenging for the users (Nelson, 2020). Therefore, users with high skills and map literacy may be considered an appropriate and suitable audience for this kind of mapping. When considering an alternative to the two multivariate options, extrinsic and intrinsic, an available solution might be to use a simpler approach, presenting a series of univariable maps of the same territory, each representing a different variable (Nelson, 2020). This approach is helpful when showing both separate variables or for presenting changes over time (Fabrikant et al. 2008; Tufte 1990). In the latter case, an animated map is also an available solution (Nelson, 2020).

Many authors have described and discussed various designs of multivariate maps (Brewer & Campbell 1998; Carr 1991; Carr, Olson & White 1992; Cuff, Pawling & Blair 1984; Dahlberg 1981). Elmer (2013) developed a taxonomy of bivariate symbol solutions on the basis of visual variables and spatial reference (points/lines/areas), and it included over 40 mapping solutions. Recently Strode et al. (2020) discussed multivariate mapping techniques suitable for visualising a vulnerability index: bivariate symbols, cartographic glyphs placed in multiple small cells to represent four variables, and Euler diagrams to depict overlap between the mapped variables.

When discussing multivariate mapping, a map user should also be taken into consideration. These kinds of maps are meant to support the comparison of phenomena. However, while working, a user may conduct various map reading operations: extract either correlational or individual information. Task types can also be distinguished based on how many variables they refer to (similar to the division of tasks applied in the study of Šašinka et al. 2021). Nelson (2000a, 2000b) used more detailed list of tasks: baseline, filtering, redundancy and condensation tasks. The baseline and filtering tasks focus on one specific variable. Baseline tasks require users to recognise one symbol, whereas filtering tasks involve distinguishing the searched variable among others presented. Redundancy and condensation tasks pinpoint a specific type of interaction between variables: redundantly paired variables for the former, and changing independently for the latter. Therefore, when evaluating the different multivariate map types, the factor of task type should also be included.

Multivariate mapping has been the subject of empirical evaluation. Bivariate choropleth maps have received the most attention while conducting empirical assessment (Carstensen 1982, 1984, 1986a, 1986b; Lavin and Archer 1984; Leonowicz 2006; Olson 1981; Šašinka et al. 2019, 2021). The research focuses on evaluating design solutions, such as an unclassed bivariate choropleth map using crossed-line shading (Lavin and Archer 1984) or on searching for factors affecting the interpretation of this map type – for example, users’ abilities (Carstensen 1982), the operation to be conducted (Carstensen 1984, 1986a), or the applied scaling method (Carstensen 1986b). Efforts have been made in order to evaluate the intuitiveness of colour scale for bivariate choropleth maps (Olson 1981; Wainer & Francolini 1980; Eyton 1984) often proving a color spectral scheme as not appropriate. Bivariate maps were also tested with regard to searching just noticeable differences – for example, for sector sizes on two-sectored pie charts (Slocum 1981).

Nelson conducted a series of experiments in order to test selective attention theory for bivariate symbols in abstract settings (1999, 2000a) and in map settings (2000b). Selective attention theory assumes that the ability to analyse one symbol's visual variable, for example colour or size, is affected by another visual variable applied in the same symbol. The results collected by Nelson (1999, 2000a, 2000b) showed that answer times for baseline and redundancy tasks (that required attending to only one dimension while the second dimension was constant or attending to either dimension) are lower than for filter and condensation tasks (that required filter out an irrelevant dimension or to attending both varying dimensions). Furthermore, when assessing the perceptual grouping with regard to bivariate symbols in an abstract setting, Nelson (2000a) showed that most combinations of visual variables can be analysed separately by a map user. Combinations in which users could extract a particular separable variable included size/hue, value/size, value/shape, and shape/hue, whereas symbol sets composed of homogeneous combinations (size/size, value/value, hue/hue) resulted in a strong interaction. Also Elmer (2013) referred to selective attention theory when empirically testing eight bivariate map types. The study included the combination of extrinsic (choropleth and graduated symbols) as well as intrinsic (bivariate choropleth maps and rectangle) maps. These two designs (i.e. choropleth map with graduated symbols and bivariate choropleth map) resulted in below average response times. Šašinka et al. (2019) tested whether the performance effects of two types of multivariate maps – intrinsic (bivariate choropleth map) and extrinsic (graduated symbols with choropleth map) – were related with the cognitive global/local strategy. Moreover, the eye-tracking data analysis showed that intrinsic bivariate maps resulted in a higher share of time spent analysing the map legend than in the case of extrinsic maps. In the follow-up study, Šašinka et al. (2021) concluded that the intrinsic method required more time and led to higher error rates that extrinsic. The difference was less pronounced in the tasks that referred to both mapped variables.

The empirical research conducted shed light on how different bivariate maps affect the way users work. Authors of the previous studies acknowledged the impact of task types on the results while working with the multivariate maps. The studies aimed to compare different types of multivariate maps but did not involve a series of univariate maps as a baseline for the comparison.

The results showed that for expert participants, both designs of multivariate mapping (extrinsic and intrinsic) are of similar suitability for solving tasks of different complexity. Moreover, in the majority of tasks, accuracy, answer time, and difficulty while using multivariate maps (M2v and M4v) were similar compared to univariate maps (M1v), and no consistent statistically significant differences were noted. The high level of literacy enables them to extract the information of different kinds needed, from bivariate and four-variate maps, with similar effectiveness, efficiency and perceived difficulty. The difference (in accuracy and difficulty only) is only visible when extracting a separable variable (T1v) from a complex four-variate map (M4v) applying integral variables compared with a simple univariate map (M1v), which supports results of Šašinka (2019, 2021) and Nelson (1999, 2000a, 2000b). But they still needed a similar amount of time. Whereas, concerning all of the metrics, we did not find differences between univariate (M1v) and bivariate maps (M2v) using extrinsic design. This suggests that for experts the use of bivariate maps with separate visual variables is convenient and does not affect performance negatively.

Analysis of eye tracking provided more nuances in the differences between the tested map types. It showed that, even though the results were similar, the effort involved in solving the tasks was higher. For instance, interestingly, the answer time did not differ in T1v and T4v, whereas fixation duration did.

The eye-tracking data analysis confirmed the differences shown by answer accuracy and perceived task difficulty: significantly higher effort was observed when extracting information concerning one separable from a four-variate map (M4v) than from univariate maps (M1v). This confirms the opinions of Nelson (1999, 2000a, 2000b) and Šašinka et al. (2019, 2021) that intrinsic maps with integral visual variables do not facilitate reference to a single variable. Additionally, eye-tracking data analysis showed differences while solving tasks that refer to more than one variable: in T2v concerning fixation duration on the map (Figure 10), and in T2v in the case of the legend AOI (Figure 11).

A comparison of the share of fixation duration on the map and on the legend provided similar results to Šašinka et al. (2021). Intrinsic maps (M4v) resulted in a higher share of fixation duration on the map (Figure 12), suggesting more effort is given to decoding the mapped information. This was visible especially in the more complex tasks, which referred to many variables (see T2v and T4v in Figure 12). The result is thus in opposition to the assumed purpose of multivariate maps: four-variate intrinsic maps resulted in greater effort to solve more complex tasks. It also suggests that there is no direct relationship with regard to the suitability of a map between the number of mapped variables and the number of variables presented on a single map. Only in the case of bivariate maps (M2v), for tasks involving two variables (T2v), was the share of legend the lowest compared to other tested map types (Figure 12). However, the other types of tasks (when referring to one and to four variables) resulted in a different tendency: for simple tasks, all of the maps had a similar share of fixation duration, whereas for complex tasks and referring to four variables, the lowest share of fixation on legend was observed in the case of a series of univariate maps.

The bivariate extrinsic maps with configural and separable visual variables (M2v) did not differ in the majority of analysed metrics from the simple univariate maps (M1v). Therefore, applying a bivariate extrinsic map instead of a univariate series of maps should not affect the performance of experienced users. The results showed that the series of univariate maps (M1v) can be helpful for both simple (T1v) and complex tasks (T2v, T4v). However, four-variate maps (M4v) did not prove such wide usability with regard to task complexity, whereas bivariate maps with separable variables (M2v) turned out to be a competitive solution for both simple (T1v) and complex tasks (T2v, T4v). Therefore, the cognitive load connected with multivariate mapping affected the performance of expert users only in the case of the four-variate intrinsic map.

The study conducted here aimed to compare the effect of applying three designs of multivariate mapping to tasks of different complexity. Expert users employed the tested maps with similar effects; however, the effort put in solving the tasks differed. In most cases the most challenging solution was a single four-variate intrinsic map, also for complex tasks, as this solution resulted in the highest effort, which was reflected, for example, in the fixation duration on the map with a legend or on the share of fixation duration on the legend. The intrinsic design is a challenge even for experienced users but does not significantly affect the results of working with a map.

Our study, as most others, has some limitations. The first one is the number of participants. To combat the limitation, we applied within-subject design, and therefore the compared groups had three times as many participants as would have been the case in a between-subject study design. Even so, we are aware that conclusions should be carefully formulated. Moreover, we applied limited eye-tracking analyses among the many available metrics. We decided to select the fixation duration metric only since we treated eye-tracking data as a support for the evaluation with usability performance metrics. We did not hypothesise on the cognitive processes involved in the use of the maps, the aim of the study being to compare the map designs. Finally, it should be noted that the study concerns a specific map configuration, with specific symbolization methods (choropleth mapping and proportional symbol mapping) and data content. Therefore, transferability of the collected results should be conducted in a careful way. Therefore, more research is needed to better investigate user issues when working with multivariate maps.

We believe that, due to the abundance of data, multivariate maps will still be needed; it is therefore important to make informed decisions when choosing map design. We believe the study conducted here provides input into understanding how to design helpful multivariate maps that might be a useful tool when making decisions on different levels of complexity: from simple to complex ones referring to many variables at once. We thus believe that further investigations and more empirical research, including specific groups of users and specific kinds of data, will enable us to further develop the understanding of multivariate mapping and usage.