Re: [QCA] model ambiguity/tied redundant prime implicants

[Adrian Dușa]

Hello Alexander,

I confess to not quite understanding what you mean by "redundant prime implicants".

By definition, a prime implicant is non-redundant, otherwise it would be minimized (and hence it would not be a prime implicant).

Furthermore, you mention "these 2 (actually 3 sets)". To which sets are you referring to?

Also, all solution models are equally long (also by definition). So to which of these solution models are you referring to by going for "the shorter solution"?

All the best,

Adrian

On Fri, Oct 27, 2023 at 9:01 AM Alexander Strelkov <alexander....@gmail.com> wrote:

Dear group members, Dear Adrian, good evening

      I have a question concerning potential model ambiguity.

Here is outcome of my calculations (sufficiency, absence of outcome).

From C1P1, C1P2: M1: ~StrongLinks*~HighFDI + ~StrongLinks*~HighESIF + HighInv*~HighFDI*~HighESIF + HighInv*~HighFDI*~LOWFLOW -> ~HighPatent inclS PRI covS covU --------------------------------------------------------- 1 ~StrongLinks*~HighFDI 0.827 0.717 0.574 0.031 2 ~StrongLinks*~HighESIF 0.886 0.815 0.696 0.153 3 HighInv*~HighFDI*~HighESIF 1.000 1.000 0.603 0.061 4 HighInv*~HighFDI*~LOWFLOW 1.000 1.000 0.422 0.031 --------------------------------------------------------- M1 0.835 0.743 0.909

From C1P3, C1P4: M1: ~StrongLinks*~HighESIF + HighInv*~HighFDI*~HighESIF + HighInv*~HighFDI*~LOWFLOW + (HighInv*~StrongLinks*~HighFDI) -> ~HighPatent M2: ~StrongLinks*~HighESIF + HighInv*~HighFDI*~HighESIF + HighInv*~HighFDI*~LOWFLOW + (~StrongLinks*~HighFDI*LOWFLOW) -> ~HighPatent ------------------- inclS PRI covS covU (M1) (M2) -------------------------------------------------------------------------- 1 ~StrongLinks*~HighESIF 0.886 0.815 0.696 0.213 0.244 0.213 2 HighInv*~HighFDI*~HighESIF 1.000 1.000 0.603 0.061 0.061 0.061 3 HighInv*~HighFDI*~LOWFLOW 1.000 1.000 0.422 0.031 0.031 0.031 -------------------------------------------------------------------------- 4 HighInv*~StrongLinks*~HighFDI 0.941 0.876 0.482 0.000 0.031 5 ~StrongLinks*~HighFDI*LOWFLOW 0.889 0.780 0.482 0.000 0.031 -------------------------------------------------------------------------- M1 0.883 0.812 0.909 M2 0.883 0.812 0.909

The fact that I have these 2 (actually 3 sets), is it linked to tied redundant prime implicants? If so, can I just go for the shorter solution? ("theory" doesn't provide clues to give preference for any model)

Many thanks for your advice!

Best wishes,

Alexander

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[tocfo...@gmail.com]

The C1P1, C1P2 information for the first intermediate solution, and the C1P3, C1P4 information for the other two shows that there is one conservative model and four parsimonious models. Intermediate solutions are derived relative to a pair of a conservative solution and of a parsimonious solution. Here, it happens that the pairs C1P1 and C1P2 lead to the same intermediate solution. The pairs C1P3 and C1P4 lead to two different intermediate solutions. This means you have model ambiguity for the parsimonious solution, which here implies model ambiguity for the intermediate solution. There is two-fold intermediate model ambiguity, for lack of a better term. The two pairs C1P1, C1P2  and C1P3, C1P4  represent model ambiguity. For the pairs C1P3, C1P4, you have additional model ambiguity because you get two intermediate solutions for C1P3, C1P4, as opposed to C1P1, C1P2. Besides all this, there is no way to get s ahorter intermediate model. The only way to shorten the models is to use the parsimonious models for interpretation.

Regards

Ingo

[Adrian Dușa]

Well, I believe "better" is a relative term.

If you're interested in the shortest possible solution then yes, the parsimonious one is the shortest.

However, as the QCA theory points for a very long time, the parsimonious solution uses untenable, impossible, contradictory and difficult counterfactuals that normally would not lead (or it is very difficult to imagine leading) to the presence of the outcome in order to be used in the minimization process.

That is the very reason why the intermediate solution was invented for.

Another possibility to get the shortest possible solution without using directional expectations is to compute the "enhanced" parsimonious solution, that is excluding what you believe are (for instance) impossible counterfactuals.

In the R package QCA, the function findRows() will help you identifying those types of counterfactuals that should be feeded to the "exclude" argument in the truthTable() command.

I hope this helps,

Adrian

On Fri, Oct 27, 2023 at 6:07 PM Alexander Strelkov <alexander....@gmail.com> wrote:

Dear Ingo, thank you very much.

   So, if I understand you correctly in my case its better to just go for a parsimonious solution (see below)

inclS PRI covS covU (M1) (M2) (M3) (M4) ------------------------------------------------------------------------------------- 1 ~StrongLinks*~HighESIF 0.886 0.815 0.696 0.091 0.153 0.153 0.152 0.152 2 HighInv*~HighFDI*~LOWFLOW 1.000 1.000 0.422 0.031 0.031 0.092 0.031 0.092 ------------------------------------------------------------------------------------- 3 ~StrongLinks*~HighFDI 0.827 0.717 0.574 0.000 0.031 0.031 4 ~StrongLinks*LOWFLOW 0.819 0.696 0.544 0.000 0.031 0.031 5 HighInv*~HighFDI*~HighESIF 1.000 1.000 0.603 0.000 0.061 0.061 6 ~HighFDI*~HighESIF*LOWFLOW 0.948 0.876 0.542 0.000 0.061 0.061 ------------------------------------------------------------------------------------- M1 0.835 0.743 0.909 M2 0.835 0.743 0.909 M3 0.883 0.812 0.909 M4 0.883 0.812 0.909

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Adrian Dusa
University of Bucharest
Romanian Social Data Archive
Soseaua Panduri nr. 90-92
050663 Bucharest sector 5
Romania

https://adriandusa.eu

[Adrian Dușa]

Ingo has already explained most of this, I would only touch upon the idea of "selecting" one of the intermediate solutions.

In Ragin's original fs/QCA software, the prime implicants chart is solved by manually selecting some (not all) of the prime implicants, so that a solution usually presents a single model.

The R package QCA deliberately presents all possible combinations of prime implicants that equally explain (cover) the initial positive evidence configurations. That leads to a lot of model ambiguity, which is not the case in fs/QCA for the simple reason there are much fewer prime implicants.

How does the researcher select the PIs?

As far as I understand, based on theoretical relevance.

Which leads to selecting one model out of many, in case of model ambiguity in R. The same thought process can be applied: the researcher purposely selects that model that makes most sense, a model that has the highest theoretical relevance.

If my understanding is correct, one can select (and methodologically discuss) a certain model out of many.

But this is very far from selecting a model just because it is the shortest. A short model is not always theoretically "sound", for the reasons I explained in the previous email.

I hope this helps, again,

Adrian

On Fri, Oct 27, 2023 at 6:07 PM Alexander Strelkov <alexander....@gmail.com> wrote:

Dear Adrian, I am posting here my expanded query as you suggested.

The results in my previous email are derived from:

intern2<-minimize(TT2n, details = TRUE,include = "?",dir.exp = "~HighInv,~StrongLinks,~HighFDI,~HighESIF,~LOWFLOW",row.dom = TRUE)

I am searching for an intermediate solution for the absence of outcome

My questions in relation to it:

Point 1. I have my results in several "sets". M1 from C1P1, C1P2 &  M1 and M2 from C1P3,C1P4. What is C1P1 etc? Is it (as stated in your book) that these are combinations of conservative and parsimonious solutions which I receive while trying to calculate my intermediate solution? And if so, why do I have  these two "sets" of causal pathways? Another person I talked to (he is using QCA but not with R) suggested that perhaps having these two sets is because of "tied redundant prime implicants" but he was not sure, it was an idea

Point 2: Both solutions are long and I seem to have what is called "model ambiguity" (I am referring to a section in Oana/Schneider/Thomann book here), so I need to make a choice which solution I take to interpret by results. For me there are no conceptual/theoretical grounds to prefer one over the other but the first solution (M1 from C1P1/C1P2) is shorter, has 4 causal pathways instead of 5 and has fewer factors in most pathways. The cases themselves are identical for both solutions (M1 from C1P1/C1P2 and M1/M2 from C1P3/C1P4). Basically, can I simply base my analysis on the first solution because its shorter and I have no better reasoning to my choice?

Many thanks for your time and apologies for potentially convoluted language,

Alexander

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