Quantifying Patterns in Mortuary Practices: An Application of Factor Analysis and Cluster Analysis to Data From the Taosi Site, China

2.1 Factor Analysis

Factor analysis examines the dependencies within a correlation matrix of original variables and attributes a number of variables with intricate relationships to new dimensions called factors. These factors elucidated and explained in detail with regards to their potential relationships between variables (Baxter, 2015; Jolliffe, 2002; Shennan, 1988; VanPool & Leonard, 2011). In archeological research, factor analysis is widely used to investigate common factors representing underlying dimensions in archaeological attributes and to elucidate socio-cultural mechanisms behind such dimensions (McHugh, 1999). Factor analysis was applied to archaeological research in the 1960s and became particularly popular in the 1970s (Doran & Hodson, 1975; Vierra & Carlson, 1981). Especially in burial studies, factor analysis has been considered an important method. Factor analysis can summarize the common meanings of attributes in a burial through the structure of their interrelationships. These common meanings represented by factors may reflect certain social relationships or social meanings, such as gender and age divisions, evidence of chronological change, or evidence of vertical status differences (Baxter, 1994; Parry & McArdle, 1991; Tainter, 1975, 1978). For example, Vehik (1977) applied factor analysis to study the 24 burial mounds and cairns in southwest Missouri (AD 500–100). He observed that factor analysis allowed him to classify three temporal groups within the burial complex based on different factors, indicating different trade relationships. Furthermore, factor analysis of grave goods groups can also detect a fraction of the potential markers of different groups in delineating ethnic and social structures (Korokhina & Grechko, 2021).

There are also many researchers who have adopted similar research methods for use in mortuary analysis, such as principal component analysis (PCA) and correspondence analysis; both of which employ a similar dimensionality reduction thinking to represent complex relationships of variables in a manageable way (Greenacre, 1984; Baxter, 1994; He, 2019). PCA can condense the original complexities in data into several principal components through matrix transformations and investigate the linear combination of each principal component with the original variables (Shennan, 1988). However, each original variable has a certain loading in the principal component, and the distribution of the magnitude of these loadings is not clearly demarcated, making it difficult to clearly express which original variables are represented by each principal component. Therefore, the extracted principal components cannot clearly explain what they represent. Most results of PCA are used as mediators for other analyses (McHugh, 1999). CA is a method of studying categories data and can be seen as “an attempt to define new variables that explain as much as possible of the departure of a table from the form it would have If there were no association between rows and columns” (Baxter, 1994, p. 114). It can suggest the relationship between variables graphically but do not give a specific statistic to measure this correlation.

With such consideration, although the above two analysis methods can analyze the relationship between variables, they are inferior to factor analysis in terms of interpreting the meaning of the results. In particular, factor analysis can more clearly explain the social meaning of the common factors through the factor rotation (Jolliffe, 2002). Therefore, factor analysis is a more suitable method for burial research and utilized in this study.

In recent years, factor analysis has been used in studies on Chinese burials. Shelach (2001, 2016) used factor analysis in his study on the Chinese Bronze Age burials in Inner Mongolia. He concluded that status and gender identity were the most obvious differences among the burials and that differences in social status also shaped the different artifact combinations. In addition, Jaffe (2012) used factor analysis to examine Chinese Western Zhou tombs, and based on the variation and combination of factor scores, he found that there were burial groups with different orientations in the same cemetery. These groups represented the identities of local burial systems that were different from the central dynastic system of the Western Zhou. Therefore, factor analysis can provide a bottom-up approach to burial research, circumventing the bias associated with the top-down approach inherent in previous studies (Jaffe, 2012; Jaffe & Cao, 2018). Thus, factor analysis is appropriate to examine a complex set of burial data to determine their potential relationships and possible patterns.

2.2 Cluster Analysis

Cluster analysis is a common quantitative classification method based on internal similarity and partitioning between groups to categorize data into different groups (Rencher & Schimek, 1997). Archaeologists usually use cluster analysis to divide various archaeological data into groups of certain significance; it has been widely used in studies on burial data (Clark, 1969; Tainter, 1975; VanPool & Leonard, 2011).

However, the interpretation of the cluster results is surrounded by some controversy. Many archaeologists believe that cluster analysis may create communities that do not exist in the real world (Baxter, 2015). While this could happen sometimes, archaeologists must make appropriate adjustments to the clusters based on the cultural context, such as adjusting the criteria for classification thresholds based on the context, when interpreting results (Tainter, 1975). Despite such concerns, cluster analysis provides archaeologists with an operational quantitative classification method with clearly defined boundaries.

Based on the different functions and characteristics of the abovementioned methods, this study uses a combination to classify burials. Such a combination assesses burial behavior as a whole, comprehensively examines the correlations between burial attributes and extracts interlinked factors for cluster analysis. Such a method focuses on the possible common orientations and patterns contained in the data set with minimal human intervention, summarizes them, and creates an effective and quantifiable classification.

5.1 Factor Analysis Results

Factor analysis extracted three common factors (whose eigenvalue values are larger than 1) from the burial sample, explaining 60.38, 15.36, and 9.65% of the relationship among variance and more than 85% in total (Figure 2).

Figure 2

(a) The eigenvalues of factor analysis and (b) the component plot in rotated space.

Furthermore, this study utilizes rotation of factors to elucidate clearer social meaning of the factors extracted (Baxter, 1994; Jolliffe, 2002; VanPool & Leonard, 2011). VARIMAX is used to do rotation, which is effectively used in most cases of previous research (McHugh, 1999).

After rotating the factors and eliminating relatively uncorrelated attributes (Figure 2b and Table 3), it was observed that factor 1 embodied mainly indicators of labor inputs, such as area and wood vessels for eating and drinking functions. Therefore, factor 1 is likely to depict the tomb owner’s financial power and their ability to feast. Factor 2 is mainly related to stone tools, especially stone weapons and the total number of grave goods. It is implied that the number of stone tools is closely related to the total number and factor 2 mainly represents a military force. Factor 3 contains variables with special functions, such as jade and musical instruments. Furthermore, the area factor has been included in factor 3, indicating a relationship with labor input. Jade and musical instruments from Neolithic China were considered a symbol of power in Neolithic China. Most noble burials were accompanied by musical instruments or large amounts of jade to represent their political nobility or religious status (He, 2018; Liu & Chen, 2012). Therefore, factor 3 could represent superiority in the realms of the political and religious.

5.2 Cluster Results

Factor scores that influenced each burial were the basis for conducting cluster analysis (Figure 3). Euclidean distance (the most common type of distance applied in clustering studies) and average linkage clustering method (which can avoid over-compression or expansion of the variable space to some degree) were utilized in this cluster analysis (He, 2019). When the threshold value was greater than 5, the clustering results could be divided into three large categories (Table 4), wherein cluster A consisted of four relatively independent burials. The discriminant analysis has proved the validation of this clustering result (Chen, 2005). The specific result is shown in Appendix 3. These burials displayed the largest labor input characteristics, that is, the largest burial area, a wide variety of burial objects, and numerous styles. In the previous classification of burials, cluster A burials – with the highest status – were those of the rulers of Taosi society (Zhongguo et al., 2015). Cluster B contained few burials and displayed a large labor input, especially in terms of pottery and woodwares, which may be related to special status. Cluster C contained the largest number of burials and was significantly different from A and B. This group has a relatively small labor input, which implies that this category differs from A and B in terms of rank or social identity. The differentiation of the three clusters is consistent with previous research on the pyramidal structure of Taosi society (Miyamoto, 2005). This means that burials at the top represent the minority of the society and contain the most complex social information that allows them to exist independently from other burials.

Figure 3

The cluster results are based on factor scores for each burial (seven groups have too many members; to better display the results appropriately and save space, some members have been omitted from the figure; the completed results have been included in the supplementary materials).

To further examine the groups in the non-elite burial category, cluster C was examined separately. Cluster C was divided into seven groups when the threshold changed to around 1. A consistency test measured whether the above grouping was scientific. Table 5 indicates that the mean and median values were significantly different between the groups, which proved that group C was statistically correct.

5.3 Further Explanation and Possible Social Meaning of Classifications

The results presented above constitute a preliminary classification of burials in the Taosi cemetery, and the different factor composition in each group represents the different types of burials and their respective characteristics.

Cluster A: The highest class of burials. As mentioned earlier, this cluster is characterized as having the largest area and the richest variety of burial objects and styles (Table 4). Furthermore, the most obvious feature that distinguishes it from other types is the presence of musical instruments. These also included a large number of weapons and feasting-related vessels. As mentioned in previous studies, these burials belong to the rulers of Taosi society. The significant variance of the factor scores of cluster A implies people’s different preferences, irrespective of their social class.

Cluster B: This group is characterized by extremely large factor 1 values, with relatively small scores for factors 2 and 3. This indicates that group B is characterized by a large number of pottery and woodwares, especially cuisine-related vessels, while other kinds of burial objects, especially jade and decorations, were rare. The members in this cluster belonged to the early period of Taosi society. These burials are also of a large size. This group indicates that there was a group of elites in the early period who were honored with only feasting-related vessels (Figure 4).

Figure 4

Variation of factor scores in each burial group (a) factor 1; (b) factor 2; and (c) factor 3 (because of the large factor variation, they are not shown in the box plots to influence the comparison between the small values of other groups).

Cluster C: This group has the largest number of tombs, including different trends of grave assemblages, which may represent different vertical and horizontal divisions. This group was further divided into seven subgroups (Table 6).

C-1: Compared to the burials in group B, group C1 embodies the opposite characteristics. This group has a very small factor 1 score and large factor 3 score. This represents a high number of jade vessels, especially jade ornaments, and jade tools (Figure 4c). This group does not contain pottery or woodware vessels. Such preferences indicate that this group of tombs emphasize the significance of jade decoration in mortuary practice.

C-2 and C-3: These groups have similar factor score combinations, with relatively high factor 2 and low factor 3 scores (Figure 4b and c). This indicates that they favored more weapons and stone tools. They contain more weapons than other groups in cluster C and represent the same group of people who shared the same burial preferences. As for the differences between these groups, the scores of factor 1 are higher for C-2, which may indicate that the tomb owners of C-2 were somewhat richer than those of C-3.

C-4: Based on the comparison of grave goods, this group may represent a statistical error and have no practical meaning.

C-5, C-6, and C-7: These groups have a small variation in factors and represent small-scale burials. Only factor 3 scores have depicted differences among these three groups (Figure 4c). C-5 included a certain number of jade decorations and no cuisine vessels. This combination of burial goods is similar to C-1, where the scale is smaller. C-6 and 7 contain only a few burial artifacts.

It can be observed that among the subgroups of cluster C, C-2 and 3 and C-1 and 5 have a consistent tendency of factor composition; therefore, they can be integrated into one group with minor internal differentiation based on the number of particular objects. C-6 and 7 represent the poorest burials as evidenced by the simple composition of burial objects (Figure 5).

Figure 5

Final classification of burials in Taosi cemetery and possible implicated social structure.

In summary, the Taosi burials can be divided into three major types, that is, A, B, and C, which correspond to large differences in labor inputs that supports the social stratification represented in previous studies. However, type C was further divided into four major categories according to different combinations and quantities of burial objects. Each of them represents a different burial tendency and social group.

6.1 Social Differentiation in Taosi Society as Reflected Through the Burials: Differences in Social Hierarchy and Identity

The pyramidal social structure has been confirmed by the burial classification structure observed in this study. In Taosi society, there was a clear vertical hierarchy of burials, evidenced by the vastly different labor inputs (Table 4). In type A, which represents the rulers of Taosi society, burials included the richest resources. The wealthy status is reflected by the total amount of burial objects and the large burial area. This mortuary tradition is similar to the other Neolithic chiefdoms in China such as the Liangzhu society (Qin, 2013; Renfrew & Liu, 2018) and Shandong Longshan societies (Underhill, 2000). Interestingly, unlike these chiefdoms, the Taosi rulers preferred to be buried with sets of cuisine vessels, including drinking and serving vessels, and kitchen-related items. During the Neolithic period, feasting was considered an effective way for the elite to demonstrate their political or economic power and negotiate social relations (Bray, 2003; Dietler & Hayden, 2010). Therefore, the presence of complete cuisine sets represents the superb feasting ability of the rulers and their high social status. Besides feasting goods, musical instruments became another significant ritualistic object in these burials, symbolizing the status of the chief in Taosi society. Burials in the next highest rank, that is, group B, have lesser total labor input than group A. They included a large number of wood and pottery vessels, which could be equal to group A burials. This proves the importance of feasting capacity in the society. Sets of pottery and wood cuisine goods became a common feature of elite burials. Unlike group A, group B did not have jade decorative objects and musical instruments. In traditional Chinese burial studies, jade and musical instruments are commonly regarded as prestigious goods. They are highly ritualistic and closely associated with religion such as the Liangzhu Culture. The difference between the two types of artifacts of groups A and B also highlights the rank differentiation among the elites. The ruler possessed the power of religious rituals in addition to enjoying great feasting abilities and secular dominance. The secondary elite possessed secular power and wealth but had no advantage in terms of religious rituals. Group C is clearly characterized by smaller and a lesser number of funerary objects. This represents a group of non-elite individuals and occupies 93% of all burials. This group represents the dominant group in Taosi society.

However, in contrast to the previous approach, the existence of diverse identities of inhabitants beyond the elite group is also reflected through this classification.

Compared to the large size and various grave goods, burials categorized under group C with low labor expenditure display their own identity through different burial assemblages. Different burial assemblages were not due to the diverse ethnic groups of Taosi cemetery. The highly consistent burial orientation and shape of the Taosi cemetery, with a clear arrangement plan mentioned in previous studies, indicates that the Taosi cemetery was a communal cemetery. Furthermore, the human bone evidence proves that there was no obvious migration from other distant areas (Zhongguo et al., 2015). Therefore, social identity sufficiently explains the different preferences for burial assemblages. Groups C-2 and C-3 represent that section of the society which tended to be buried with weapons; they could have belonged to a military-related group. Based on the area and different pottery, there was a division in power and status among this group, wherein burials of senior warriors included certain financial resources, as well as people who generally did not have the financial means to feast. Burials in groups C-1 and C-5 did not attach importance to the ability to feast and did not include serving or drinking vessels. Instead, they attached great importance to jade and decorations. Similarly, a hierarchical division is also observed based on the different amounts of jade and the burial size. As mentioned above, some jade is closely related to religion in Neolithic China, and jade decorations also represent a certain level of social power and special social status (Qin, 2013). So the owner of this group may be a group of people who had certain religious power in the Taosi society.

The classification of burials proves that there was a two-axial social differentiation in the Taosi society (Figure 5). The vertical differentiation of social status represents the power stratification, that is, from the rulers to the elites to the commoners. Horizontal differentiation represents the division of different social identities. The three categories of burials were weapons-orientated, jade-orientated, and small burials. Furthermore, there are internal divisions within these groups. Such a diverse composition of burial types and group differentiation represents a high degree of complexity in Taosi society.

6.2 The Advantages and Disadvantages of Multivariate Analysis

The multivariate method provides a clear classification logic and investigates the patterns underlying burial behavior. In the traditional method, the Taosi cemetery’s size is used as the primary criterion to classify major categories. The burials and assemblages of different grave objects are added to the already classified framework. Due to this, when an assemblage did not completely correspond with a category, they were forcibly included to produce a specific type of result. Such bias explains why the classification boundary of the traditional method was blurred, and burials in the same category could not meet the classification interpretation. Factor and cluster analyses could detect mortuary patterns hidden in the variables without any presupposition and follow scientific, statistical logic.

Furthermore, compared to the traditional method, multivariate analysis can reveal more detailed information about mortuary practice and society. Although there is a certain connection between burial area and social rank, the size of the burial can only explore the division of social structure in a broad sense. Burials with obvious gaps can be divided by the attribute of area. Results of groups A and B are consistent with previous traditional results. However, when it comes to non-elite burials, the size attribute and the number of burial goods cannot fully explain the complexity of burials because burials have demonstrated a proclivity for different burial assemblages. Therefore, the traditional qualitative method is not suitable to classify small burials because much attention is paid to the area factor, which neglects burial goods and their combinations. This is where the results of the two methods differ. The multivariant method is better for exploring the different group compositions of non-elite burials. The groupings do not have any preconceptions or interventions that allow empirical judgments to misinterpret the data in certain societies. Furthermore, instead of the simple top-bottom grouping, the research also considered the principle of labor input along with the symbolic principle to determine the potential patterns of mortuary practice.

However, this method has a few disadvantages. Quantitative analysis is an examination of numerical values and is less sensitive to too small changes. Such drawbacks have also been pointed out by statisticians (Dash, Liu, Scheuermann, & Tan, 2003; Halkidi, Batistakis, & Vazirgiannis, 2001). The algorithm of hierarchical cluster analysis due to inefficient validation and lack of accuracy, mainly in the form of the lower clusters in small sized usually are too close to other clusters, which then increases the uncertainty of the clustering results. Often, complex burial information and burials with a larger number of burial objects can be clearly classified. Therefore, all the A-class burials were returned separately due to the unequal information of large and small burials. If the classification is conducted, there is further analysis of small data in conjunction with the archaeological context. This is why the threshold of clustering analysis becomes smaller due to small burials to examine more subtle changes.

Furthermore, the interpretation of clustering results cannot be separated from the traditional combination of qualitative analysis and archaeological contexts. In interpreting the results, the remains are archaeologically rich enough to examine the social information behind the groupings. Although quantitative classification can be informative, the purpose of the classification is not only to divide but also to explain the social information behind the burial behavior. For example, when sets of eating and drinking vessels are understood as embodying powerful feasting capacities associated with political regulation, jade burial groups with specific religious power and other information are inseparable from the special social meaning embedded in the previous qualitative examination. In quantitative methods, especially clustering processes, there are no predefined categories and no examples to show what kind of ideal relationships should exist between the data (Halkidi et al., 2001; Kaufman & Rousseeuw, 2009), so the validation of the statistical results in archaeology research must be done with specific social practices and cultural context as verification. Therefore, future research must remember that neither quantitative nor qualitative methods alone can explain complete burial behavior. Therefore, an effective combination of both is required.