The data of the 103 living units applied to calculate the MCA and AHC include variables with a total of categories. The frequency distributions of the categories are displayed in Table 2.
Relations between the characteristics and the living units: results of the MCA
The calculation of the total inertia of the data amounts to and is distributed over a total of eigenvalues. The average eigenvalue is and explains 4.93% of the total inertia.
Table 3 illustrates the proportion of explained inertia for each axis in decreasing order and thus provides the information needed to make decisions about the number of axes to be included in the analysis. The second axis brings the cumulated modified inertia rate to 90.90%. Therefore, only the first two axes will be interpreted in the results of the MCA.
The first axis explains 17.44% of the total inertia, and the second axis explains 13.76% of the total inertia. Thus, the MCA map (Fig. 1) represents 31.21% of the total inertia. For the interpretation of the principal axes, the categories that contribute significantly to the explanation of the principal axis are informative. These include all categories whose contribution exceeds the average contribution of 2.56%.
Figure 1: MCA map for the superimposed representation of living units (blue points) and structural characteristics (red triangles).
The first principal axis applies to the following categories: “living unit has a size ≤ 15 beds” (Size 0), “living unit is additionally financed” (Finance 1), “living unit has only single rooms” (SRoom 1), “nurses do not work exclusively in one unit” (AssignN 0), “lunch is cooked in the kitchen of the unit” (Selfcook 1), “a registered nurse is not always present” (PresenceRN 0), “all meals are served homestyle on the table” (Mealserv 1), “segregated living concept” (Segregative 1), “do not exclusively have single rooms” (SRoom 0), “living unit has a size > 15” (Size 1), “residents-per-service staff member ratio is less than or equal to the median” (SSMRatio 1), “residents-per-service staff member ratio is greater than the median” (SSMRatio 0), and “integrative living concept” (Segregative 0). The categories are sorted according to their contributions, so that the first category Size 0 explains the main contribution to the first axis. A substantial contribution to the second principal axis is made by the following categories: “no special qualification in psychogeriatric care” (Jobqual 0), “segregated living concept” (Segregative 1), “built specially for people with dementia” (Build 1), “is additionally financed” (Finance 1), and “living unit has a size ≤ 15” (Size 0). These categories each explain between seven and ten percent of the second principal axis.
The categories that are close to each other, such as “living unit is additionally financed” (Finance 1), “special qualification in psychogeriatric care” (Jobqual 1), “living unit is protected by exit controls” (Guarded 1), etc. are correlated positively with each other and describe the corresponding living units in this area.
Binary categories always correlate negatively and are located opposite to each other. Most of the living units that are distinguished by the binary categories are scattered in the left and right upper areas of Figure1. These living units differ significantly from the living units displayed on the second principle axis below the centroid.
Identifying the types of living units: results of the AHC
The numbers of clusters with the highest percentage decrease in the gain of the between-clusters inertia are marked by a bend (elbow criterion) in the curve of the inertia gain in Figure 2. For this reason, three clusters were chosen. The proportion of "between-clusters inertia" that can be measured is 25.41% for a three-cluster solution.
In our analysis we choose 11 axes to calculate the AHC that summarize 83.71% of the total inertia.
Figure 3 displays the convex hulls of the three cluster solutions in the correspondence space of the MCA map. The two clusters in the upper left (living units = circles) and upper right area (living units = squares) differ in the first dimension. These clusters are related to the categories that make a significant contribution to the first principal axis.
The largest cluster (living units = triangles) is close to the centroid and differs in the second principle axis. This cluster represents the average living unit type and is associated with the categories that contribute significantly to the second principal axis.
By applying the v-test, the structural characteristics that clustered the respective living units were determined. The test results show that each of the three clusters in Figure 3 occurs with a specific combination of categories. Table 4 illustrates these combinations, which leads us to the content-related definition of our three cluster types. We designate the three clusters as "house community", "dementia special care units" and "usual care".
The categories in Table 4 describing the clusters are sorted in decreasing order according to their significance such that the first categories have the lowest p-values as a result of the v-test. The categories (Finance 1, Size 1 and Size 0) that are most significant for their respective clusters are therefore at the head of the table. The v-test and p-values can be calculated using the R-code in the supplementary information. To present a summarized table as a result, we have decided to provide the percentages in the brackets only, as they are more descriptive for the distribution of a category.
All listed categories used to describe the three clusters satisfy the p < 0.05 requirement. With the exception of the last column, "Not significant", all categories that do not provide significant information for the clusters are displayed.
Furthermore, we observe three different cases of attributions in the categories of the clusters in Table 4. Some examples are as follows: The first case of attribution concerns categories that are only informative for a particular cluster. We describe this case as a “unique characteristic”. This applies, for example, to the “living unit is protected by exit controls” (Guarded 1) category in the "dementia special care units" cluster. The category “Guarded 1” is only significant in Cluster “dementia special care units” and not in other clusters. Therefore, we call this category “unique characteristic”. The second case concerns dichotomous categories relating to different clusters. We define this case as "strong difference". This is valid for the categories “living unit was not specially built for people with dementia” (Build 0) and “living unit was built specially for people with dementia” (Build 1) because Build 1 relates to the cluster "dementia special care unit" and Build 0 to the cluster "usual care".
The third case will be applicable when a category is related to two or more clusters. We define this case as "intersection". This applies to the category “do not exclusively have single rooms” (SRoom 0), which is indicative of both the cluster "dementia special care unit" and the cluster "usual care". However, it should be noted that the second case also applies to the category “living units do not exclusively have single rooms” (SRoom 0) because “living units have only single rooms” (SRoom 1) is informative for the cluster "house community”.
Categories describing the second case are particularly suitable for describing differences between two clusters.
Table 4 shows that these category combinations allow clear distinctions to be made from the cluster "usual care". The five top categories of the cluster "dementia special care unit" and cluster "house community" can be distinguished by the dichotomous categories of the cluster "usual care".
In contrast, the differences between the clusters "dementia special care units" and "house community" are distinguished more by their unique characteristics. This distinction is exemplified by the fact that categories such as “special qualification in psychogeriatric care” (Jobqual 1), “segregated living concept” (Segregative 1) and “living unit is protected by exit controls” (Guarded 1) are informative for the cluster “dementia special care units”, but, including their dichotomous category, have no significance for the cluster “house community”.
To further validate the identified types, we additionally conducted some descriptive analysis to describe differences between the residents who are living in the living units. The examination of the resident data shows no differences regarding the variable "sex". However, there are clear differences in the “age”, “diagnosis of dementia” and “severity of dementia”. The relative frequencies of dementia diagnosis and severe dementia are significantly higher in the “dementia special care units” cluster.
These results (resident characteristics of the three clusters of dementia special care units, usual care, and house community) are presented as a table in the supplementary information.
Comparison between the a priori defined types and the types identified by the explorative clustering technique: results of the cross table
If we compare the current types identified with the explorative clustering method to the a priori defined types, we can see that the different types of development techniques had an impact on the affiliation of the 103 living units to the types. To illustrate this, Table 5 presents a cross-table that contrasts the affiliations of the living units with the different types.
One can see that all of the living units that were formerly affiliated with the type “large segregated living units with additional financing regulated by an agreement” (LSLU II) are now affiliated with the type “dementia special care units”.
However, three living units that were formerly affiliated with the type “large segregated living units without extra funding” (LSLU I) are also affiliated with the type “dementia special care units”. It is surprising that one living unit that was formerly affiliated with the type “large integrated living units without extra funding” (LILU) is now also affiliated with “dementia special care units”. This may be explained by the fact that this living unit does not have the characteristic “segregative living concept” (Segregative 1) but is defined by the type-specific characteristics “built specially for people with dementia” (Build 1), “special qualification in psychogeriatric care” (Jobqual 1), residents-per-registered nurse ratio is less than or equal to the median (RNRatio 1), “do not exclusively have single rooms” (SRoom 0), “residents-per-service staff member ratio is greater than the median” (SSMRatio 0), “lunch is not cooked in the kitchen of the living unit” (Selfcook 0) and “large size” (Size 1).
When looking at the type “usual care”, it is clear that the majority (47 of 59) were formerly affiliated with the type “large integrated living units without extra funding” (LILU). However, 11 living units from the type “large segregated living units without extra funding” (LSLU I) are now affiliated with the “usual care” type. The type “house community” is more or less consistently compounded by living units that were formerly affiliated with the small living units (integrated and segregated without extra funding).
Again, what is surprising is that one living unit that was formerly affiliated with the type “large segregated living units without extra funding” (LSLU I) is now affiliated with the type “house community”. This can be explained by the categories “lunch is cooked in the kitchen of the living unit” (Selfcook 1), “all meals are served home style on the table” (Mealserv 1), “residents-per-service staff member ratio is less than or equal to the median” (SSMRatio 1) and “living unit is not additionally financed” (Finance 0), which were evident in this living unit.