Clustering projects according to similarities in outcomes they achieve

Among some users of LogFrames it is verboten to have more than one Purpose level (i.e. outcome) statement. They are likely to argue that where there are multiple intended outcomes a project's efforts will be dissipated and will ultimately be ineffective. However, a reasonable counter-argument would be that in some cases multiple outcome measures may simply be more nuanced description of an outcome that others might want to insist is expressed in a singular form.

The "problem" of multiple outcome measures becomes more common when we look at portfolios of projects where there may be one or two over-arching objectives but it is recognised that there are multiple pathways to their achievement. Or, that it is recognized that individual projects may want to trying different mixes of strategies , rather than just one alone.

How can an evaluator deal with multiple outcomes, and data on these? Some years ago one strategy that I used was to gather the project staff together to identify for each output, what its expected relative causal contribution was of each of the project outcomes. These judgements were expressed in individual values that added up to 100 percentage points per outcome, plotted in an (Excel) Outputs x Outcome matrix, projected onto a screen for all to see, argue and edit. The results enabled us to prioritise which Output to Outcome linkages to give further attention to, and to identify, in aggregate, which Outputs would need more attention than others.

There is also another possible approach. More recently I have been exploring the potential uses of clustering modules within the RapidMiner data mining package. I have a data set of 34 projects with data on their achievements on 11 different outcome measures. A month ago I was contracted to develop some predictive models for each of these outcomes, which I did. But it now occurs to me that doing so may be somewhat redundant, in that there may not really be 11 different types of project performance. Rather, it is possible that there are a smaller number of clusters of projects, and within each of these there are projects having similar patterns of achievement across the various possible outcomes.

With this in mind I have been exploring the use of two different clustering algorithms: (k-Means clustering and DBSCAN clustering. Both are described in practically useful detail in Kotu and Deshpande's book "Predictive Analytics and Data Mining"

With k-Means you have to specify the number of clusters you are looking for (k), which may be useful in some circumstances. but I would prefer to find an "ideal" number. This could be the number of clusters where there is the highest level of similarity of cases within a cluster compared to other alternative numbers of clusterings of the same cases. The performance metrics of k-Means clustering allows this kind of assessment to be made. The best performing clustering result I found identified four clusters. With DBSCAN you don't nominate any preferred number of clusters, but it turns out there are other parameters you do need to set, which also affect the result, including the number of clusters found. But again, you can compare and assess these using a performance measure, which I did. However, in this case the best performing result was two clusters rather than four!

What to do? Talk to the owners of the data, who know the details of the cases involved and show them the alternative clustering, including information on which projects belong to which clusters. Then ask them which clustering makes the most sense i.e. is most interpretable, given their knowledge of these projects.

And then what? Having identified the preferred clustering model it would make sense then to go back to the full data set and develop predictive models for these clusters: i.e. to find what package of project attributes will best predict the particular cluster of outcome achievements that are of interest.

Evolving better performing hypotheses, using Excel

You may not know this, but there is an Excel add-in called Solver. This can be used to evolve better solutions to computation problems.

It can also be used to identify hypotheses that have a better fit with available data. Here is how I have been using Solver in Excel....

I start by entering a data set into Excel that is made up of cases (e.g.25 projects), listed row by row. The columns then describe attributes of those projects, e.g. as captured in project completion reports. These attributes can include aspects of the project context, the way the project was working plus some outcome performance measures.

A filtering mechanism is then set up in Excel, where you can chose a specific sub-set of the attributes that are of interest (aka our hypothesis), and then all the projects that have these attributes are automatically highlighted.

The performance of this sub-set of projects is then tested, using a simple device called a Confusion Matrix , which tells us what proportion of the selected projects have "successful" versus "unsuccessful" outcomes (if that is the outcome of interest). Ideally, if we have selected the right set of attributes then the proportion of "successful" projects in the selected sub-set will be greater than their prevalence rate in the whole set of projects.

But given that the number of possible hypotheses available to test doubles with each extra attribute added into the data set, this sort of intuitive/theory led search could take us a long time to find the best available solution. Especially when the data set has a large number of attributes.

This is where Solver helps. Using its evolutionary algorithm the Solver add-in provides a quick means of searching a very large space of possible solutions. To do this there are three parameter which need to be set, before setting it to work. The first is the Objective, which is the value you want to maximise. I usually choose the "Accuracy" measure in the Confusion Matrix. The second is the range of cells whose values can be varied. These are the ones identifying the set of project attributes, which can be used to make a hypothesis. They can be set to (1), absent (0) or not relevant (2). The third is is the Constraints, which limit the values that these variable cells can take e.g. not negative, and nothing other than these three types of values.

In the space of a minute Solver then explores up to 70,000 possible combinations of project attributes to find the combination that generate the most accurate prediction i.e. a set of projects with the highest possible proportion of "successful" projects. In my recent trials, using a real data set, the accuracy levels have been up around 90%. I have been able to compare the results with those found using another algorithm which I have written about in earlier posts here, called a  Decision Tree algorithm. Despite being quite different algorithms, the solutions that both algorithms have found (i.e. the specific set of project attributes) have been very similar in content (i.e. the attributes in the solution), and both had the same level of accuracy.

An important side benefit of this approach to finding out "what works" is that by manually tweaking the solutions found by Solver you can measure the extent to which each attribute in the winning solution makes a difference to its overall accuracy. This is the kind of question many donors want to answer re the projects they fund, when they ask "What difference does my particular contribution make?"

If you want help setting up Excel to try out this method, and have a data set ready to work on, feel free to contact me for advice: rick.davies@gmail.com, or leave a comment below

Is QCA it's own worst enemy?

[As you may have read elsewhere on this blog] QCA stands for Qualitative Comparative Analysis. It is a method that is finding increased use as an evaluation tool, especially for exploring claims about the causal role of interventions of various kinds. What I like about it is its ability to recognize and analyse complex causal configurations, which have some fit with the complexity of the real world as we know it.

What I don't like about it is its complexity, it can sometimes be annoyingly obscure and excessively complicated. This is a serious problem if you want to see the method being used more widely and if you want the results to be effectively communicated and properly understood. I have seen instances recently where this has been such a problem that it threatened to derail an ongoing evaluation.

In this blog post I want to highlight where the QCA methodology is unnecessary complex and and suggest some ways to avoid this type of problem. In fact I will start with the simple solution, then explain how QCA manages to make it more complex.

Let me start with a relatively simple perspective. QCA analyses fall in to the broad category of "classifiers". These include a variety of algorithmic processes for deciding what category various instances belongs to. For example which types of projects were successful or not in achieving their objectives.

I will start with a two by two table, a Truth Table, showing the various possible results that can be found, by QCA and other methods. Configuration X here is a particular combination of conditions that an analysis has found to be associated with the presence of an outcome. The Truth Table helps us identify just how good that association is, by comparing the incidences where the configuration is present or absent with the incidences where the outcome is present or absent.

As I have explained in an earlier blog, one way of assessing the adequately of the result shown in such a matrix is by using a statistical test such as Chi Square, to see if the distribution is significantly different from what a chance distribution would look like.There are only two possible results when the outcome is present: the association is statistically significant or it is not.

However, if you import the ideas of Necessary and/or Sufficient causes the range of interesting results increases. The matrix can now show four possible types of results when the outcome is present:

1. The configuration of conditions is Necessary and Sufficient for the outcome to be present. Here cells C and B would be empty of cases
2. The configuration of conditions is Necessary but Insufficient for the outcome to be present. Here cell C would be empty of cases
3. The configuration of conditions is Unnecessary but Sufficient for the outcome to be present. Here cell  B would be empty of cases
4. The configuration of conditions is Unnecessary and Insufficient for the outcome to be present. Here no cells would be empty of cases

The interesting thing about the first three options is that they are easy to disprove. There only needs to be one case found in the cell(s) meant to be empty, for that claim to be falsified.

And we can provide a lot more nuance to the type 4 results, by looking at the proportion of cases found in cells B and C, relative to cell A. The proportion of A/(A+B) tells us about the consistency of the results, in the simple sense of consistency of results found via an examination of a QCA Truth Table. The proportion of A/(A+B) tells us about the coverage of the results, as in the proportion of all present outcomes that exist that were identified by the configuration. 

So how does QCA deal with all this? Well, as far as I can see, it does so in a way makes it more complex than necessary. Here I am basing my understanding mainly on Schneider and Wagemann's account of QCA.

1. Firstly, they leave aside the simplest notions of Necessity and Sufficiency as described above, which are based on a categorical notion of Necessity and Sufficiency i..e a configuration either is or is not Sufficient etc. One of the arguments I have seen for doing this is these types of results are rare and part of this may be due to measurement error, so we should take  more generous/less demanding view of what constitutes Necessity and Sufficiency
2. Instead they focus on Truth Tables with results as shown below (classed as 4. Unnecessary and Insufficient above). They then propose ways of analyzing these in terms of having degrees of Necessity and Sufficiency conditions. This involves two counter-intuitive mirror-opposite ways of measuring the consistency and coverage of the results, according to whether the focus is on analyzing the extent of Sufficiency or Necessity conditions (see Chapter 5 for details)
3. Further complicating the analysis is the introduction of a minimum thresholds for the consistency of Necessity and Sufficiency conditions (because the more basic categorical idea has been put aside). There is no straightforward basis for defining these levels. It is suggested that they depend on the nature of the problem being identified.

  Configuration X contains conditions which are neither Necessary or Sufficient 

Using my strict interpretation of Sufficiency and Necessity there is no need for a consistency measure where a condition (or configuration) is found to be Sufficient but Unnecessary, because there will be no cases in cell B. Likewise, there is no need for a coverage measure where a condition (or configuration) is found to be Necessary but Insufficient, because there will be no cells in cell C,

We do need to know the consistency where a condition (or configuration) is Necessary but Insufficient, and the the coverage, where where a condition (or configuration) is found to be Sufficient but Unnecessary.

Characterising purposive samples

In some situations it is not possible to develop a random sample of cases to examine for evaluation purposes. There may be more immediate challenges, such as finding enough cases with sufficient information and sufficient quality of information.

The problem then is knowing to what extent, if at all, the findings from this purposive sample can be generalised, even in the more informal sense of speculating on the relevance of findings to other cases in the same general population.

One way this process can be facilitated is by "characterising" the sample, a term I have taken from elsewhere. It means to describe the distinctive features of something. This could best be done using attributes or measures that can, and probably already have been, used to describe the wider population where the sample came from. For example, the sample of people could be described as being of average age of 35 versus 25 in the whole population, and 35% women versus 55% in the wider population. This seems a rather basic idea, but it is not always applied.

Another more holistic way of doing so is to measure the diversity of the sample. This is relatively easy to do when the data set associated with the sample is in binary form, as for example is used in QCA analysis (i.e. cases are rows, columns are attributes and cell values of 0 or 1 indicate if the attributes was absent or present)

As noted in earlier blog postings,Simpsons Reciprocal Index is a useful measure of diversity. This takes into account two aspects of diversity: (a) richness, which in a data set could be seen in the number of unique configurations of attributes found across all the cases( think metaphorically of organisms - cases, chromosomes-configurations and genes-attributes) and (b) evenness, which could be seen in the relative number of cases having particular configurations. When the number of cases is evenly distributed across all configurations this is seen as being more diverse than when the number of cases per configuration varies.

The degree of diversity in a data base can have consequences. Where a data set that has little diversity in terms of "richness" there is a possibility that configurations that are identified by QCA or other algorithmic based methods, will have limited external validity, because they may easily be contradicted by cases outside the sample data set that are different from already encountered configurations. A simple way of measuring this form of diversity is to calculate the original number of unique configurations in the sample data set as a percentage of the total number possible, given the number of binary attributes in the sample data set (which is 2 to the power of the number of attributes). The higher the percentage, the less risk that the findings will be contradicted by configurations found in new sets of data (all other things being constant).

Where a data set has little diversity in terms of "balance" it will be more difficult to assess the consistency of any configuration's association with an outcome, compared to others, because there will be more cases associated with some configurations than others. Where there are more cases of a given configuration there will be more opportunities for its consistency of association with an outcome to be challenged by contrary cases.

My suggestion therefore is that when results are published from the analysis of purposive samples there should be adequate characterisation of the sample, both in terms of: (a) simple descriptive statistics available on the sample and wider population, and (b) the internal diversity of the sample, relative to the maximum scores possible on the two aspects of diversity.