OUT in truthtable rows

[Sarah Wang]

Hi Adrian, 

I am running an analysis and the truthtable is showing some strange things. I have attached the raw data and R codes that I have used. 

My questions are: 

1. why does the truthtable row 44 show KOR OUT is 1 while the data show KOR is out of the set?

2. why  does truthtable row 18 show USA OUT is 0 while the data show USA is in the set?

3. More importantly, is there anything alarming that I should be aware of? 

4. Could you please also suggest the way to resolve this?  (I know how to manually change the OUT from 0 to 1 or vice versa in R. Is there any other way to achieve it? )

Thank you in advance 

Kind regards

Sarah 

[tocfo...@gmail.com]

Hi Sarah,

the entries in the OUT column capture whether the truth table rows are designated as sufficient for the outcome. There are three entries (or four, depending on how one looks at this):

• 1: The configuration represented by the truth table row is sufficient.
• 0: The row is not sufficient. (which is not the same as saying it is sufficient for the negated outcome)
• ?: One can't tell because the configuration does not have any members. The ? entries are not displayed by default of the truthTable() command. Setting the argument complete = TRUE in the truthTable() function outputs all truth table rows.
• C: Stands for contradiction, which is usually not part of a truth table produced with truthTable(). It means there are members of the row, but the evidence is not clear with regard to whether the row is sufficient or not.

What the entry is that you see in the OUT column depends, at a minimum, on the chosen consistency threshold and the frequency threshold. In your case, it also depends on the PRI cutoff. If the parameters of a row are all above the threshold, it is a 1; a 0 otherwise. (assuming a rows does have at least one member and the frequency cutoff is not higher than 1) The consistency score and PRI score of a row depends on the membership of all cases in the row and in the outcome. For this reason, there is no link between the value that you see in the OUT column and the membership of a case in the outcome.

 What you write about Korea suggests that Korea is a deviant case for consistency in kind. Personally, it would see it as a problem if the only member of a consistent truth table row is a non-member of the outcome. If you want to recode row 44 as not sufficient for the outcome, you have to add this to the truthTable() command that you shared: exclude = "44"

Usually, there is no reason to recode rows with a 0 in the outcome column to 1. At least, I would not recommend here.

Kind regards

Ingo

[Adrian Dușa]

With a bit of delay (as I attend the QCA conference of the Americas), I just wanted to make an additional comment about the column "OUT".

This is not the same thing as the "outcome", it stands for (truth table) "output".

The outcome value for USA might be "in" the set (0.785) and it so happens that USA is the only case in row 18 of the truth table. But the inclusion score of that row (not case!) in (or the consistency of that row with) the outcome is 0.761 which is smaller than the cut-off value of 0.8, hence the OUTput value of that row is 0.

Row 18 is the configuration 010001, which in Boolean expression is:

pof(~track*inequa*~edmat*~selec*~privat*comp -> segr3, data = mydata)

                                             inclS   PRI   covS   covU  
-----------------------------------------------------------------------
1  ~track*inequa*~edmat*~selec*~privat*comp  0.761  0.524  0.067    -  
----------------------------------------------------------------------- 

or otherwise 

allcases <- compute(~track*inequa*~edmat*~selec*~privat*comp, data = mydata)

sum(fuzzyand(allcases, mydata$segr3)) / sum(allcases)

[1] 0.7613718

So all cases, not just USA, contribute to the consistency score of that configuration (row 18) in the outcome. It does not matter that the USA is the only case in that configuration.

To complement Patrick and Ingo's excellent description, the truth table can in fact display contradictions by specifying two values for the inclusion cut-off, something like incl.cut = c(0.8, 0.4)

I hope this helps,

Adrian

--
You received this message because you are subscribed to the Google Groups "QCA with R" group.
To unsubscribe from this group and stop receiving emails from it, send an email to qcawithr+u...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/qcawithr/5f9c3ab5-82a4-4049-9ff6-1a22a6be2314n%40googlegroups.com.

[Sarah Wang]

Hi Ingo

Thank you so much for the detailed explanation. 

Could I please ask some further questions to enhance my understanding? 

1. You mentioned about Korea, row 44: the incl 0.9596xxx is higher than my threshold that I set (0.8), PRI is 0.877 is also higher (0.51 I set). And Korea is the only case in that row. Because of these information, Korea is the problem, because it is the only member in that rom which is a non-member of the outcome. Is my understanding correct? 

If it is correct, do you know why this is happening? 

You also mentioned something about recode row 44 to 0, does it mean your suggestion to remove this problem is to change OUT to 0 for row 44 Korea? 

2. Row 18, USA, the incl is 0.7613.. from the truth table, but I set incl.cut  = 0.8, is it becasue incl does not meet 0.8 so the OUT in row 18 is 0? 

My question is why would this happen? USA is the only case in this row. Is it because the mathematically calculation behind based on the fuzzy calibration membership score?  Did you also suggest that I should not change the OUT in row 18 into 1 manually? (could you please share why you choose not to? )

Thank you so much.  

Kind regards

Sarah 

[Sarah Wang]

Sorry another follow-up question please: 

In one senario, if the OUT is 0 because the PRI for the case is lower that I set. If I manually changed this OUT to 1, what would be the consequence?  

Thank you
kind regards

Sarah 

[Adrian Dușa]

I believe my previous message (sent just minutes before Sarah's) explains the subsequent questions.

Just one word of advice: there should be no "manual" changing the output value in the truth table, and certainly not from an output value of 0 to 1.

The only consistent way to alter the output column is to use the argument "exclude", and that only for the untenable, impossible counterfactuals.

Adrian

[Sarah Wang]

Thank you Adrian. I read all your messages and they really clarify my thinking.  Thank you! 

It is a pity that I had to miss your advanced R training in the QCA Americans. I would like to attend something like this in the future when you run again. 

Kind regards

Sarah 

[Adrian Dușa]

I'd say, unless you have very good reasons to "exclude" rows, you are safe in leaving them as they are.

After all, this is what your empirical evidence shows.

Best,

Adrian

On Fri, Mar 22, 2024 at 9:26 PM Sarah Wang <sarah...@gmail.com> wrote:

Thank you Patrick and Adrian's feedback. I am much clearer in this now. 

Could I please ask what is the practice if we encounter this type of situation? 

Like in my situation of row 18 - USA, we just leave it as it is, so this case is not going to explained by any sufficient solutions? 

Row 44, I should recode it so it is removed? 

Thank you so much

Kind regards

Sarah