Intervening relationships: X1  X2  Y

News from science – what? Probability of Alzheimer’s Severity of Rheumatoid Arthritis

Nonsensical correlation What could explain this? Rheumatoid Arthritis Alzheimer’s

An illustration with a causal model There is a variable (Z) that intervenes between A and B if: A Z B

A test of whether Z intervenes between A and B Look at the relationship between A and B, controlling for Z This means, that for all values of Z, you should look at the relationship between A and B.

Scatterplot illustration of when there is an intervening relationship All people Alzheimer’s Only high levels of ibuprofen Only small levels of ibuprofen Alzheimer’s Rheumatoid Arthritis Alzheimer’s Rheumatoid Arthritis Rheumatoid Arthritis

There is a variable that intervenes between A and B if: Rheumatoid arthritis Ibuprofen Alzheimer’s NOT Ibuprofen Rheumatoid arthritis Alzheimer’s

News from science – fluoride causes cancer? Water Fluoridation Cancer rates (cities around world)

Strong correlation: causation? What could be the reason cancer rates are higher? Fluoride Cancer rates http://www.dentalwatch.org/fl/knox.pdf

Scatterplot illustration All cities Fluoridation Only poor cities Only rich cities Fluoridation Cancer rates Fluoridation Cancer rates Cancer rates

What is it? Fluoridation Wealth Cancer Wealth Fluoridation Cancer

So, what the heck? Intervening and spurious are the same empirically? So, how do we know the difference?

Spurious and intervening relationships are Observationally equivalent Theory Spurious and intervening relationships are Observationally equivalent

Here are some examples that are not observationally equivalent Perhaps there are simply alternative causes of something… Or is it intervening?

Does being white cause education which causes income? Race (being white) Education Income Income Race (being white) Education

Is this an intervening relationship Is this an intervening relationship? Being white causes education, which then causes income White Non-white High income 70 25 Low income 30 75

What are the arguments?

Is this an intervening relationship Is this an intervening relationship? Being white causes education, which then causes income Only those with high education White Non-white High income 90 60 Low income 10 40

Is education intervening? Only those with low education White Non-white High income 40 10 Low income 60 90

Conditional effects

Education causes political tolerance? Not in the former Soviet Union: Political tolerance Education

Does perceived political advantage reduce the likelihood of litigation? (in the case of the Moscow Theater case)

What causes people to litigate against their government What causes people to litigate against their government? (with regard to the Moscow Theater incident) How should this variable be measured?

Measure of litigation (with regard to the Moscow Theater incident) Are you one of the plaintiffs in this lawsuit? freq vars = litigant.

Theory from the U.S.: Political Disadvantage When people feel alienated from traditional avenues of participation or representation, then they may be more likely to participate in litigation.

Political Disadvantage Measure: the highest answer from the following two questions How well do you believe that President Putin represents your interests? How well do you believe that the current Duma represents your interests? very well, rather well, not very well, not at all well

Crosstab Analysis: Is political advantage related to litigation?

Theory People tend to use procedures that they believe will be fair Thus, perception of fairness of the courts causes litigation How carefully will the court listen to the hostages side of the story? Very carefully, rather carefully, somewhat carefully, not at all carefully

Theory Why is it that when people think the courts are more unfair, they are MORE likely to litigate? UGH! And: what? what is the reason?

Anger Could it be that the more angry people are, they more likely they want to engage in an expressive activity – In other words, litigation is not about the fairness of courts – it is about expressing how angry you are How to test that?

Perhaps the negative correlation between perceptions of fairness and litigation is particularly negative when people have reason to be angry – they are politically disadvantaged

In this case, we are testing a conditional relationship: The effect of one independent variable is intensified OR mitigated, depending on the values of another variable The negative effect of procedural justice will intensify as political advantage decreases

Perceived probability of judicial fairness Anger (political disadvantage) Litigation Proc Just Proc Just Proc Just Low anger High PD High anger High PD Med anger Med PD

A more political example… So, let’s look at the relationship between political interest and participation

Political interest Self efficacy Participation

Political interest and political participation | How much interest do you have in political polpartbes | affairs c | No intere Not very A fair am A great d | Total -----------+--------------------------------------------+---------- 0 | 174 287 61 4 | 526 | 62.59 53.35 28.64 12.12 | 49.53 1 | 40 82 30 3 | 155 | 14.39 15.24 14.08 9.09 | 14.60 2 | 64 169 122 26 | 381 | 23.02 31.41 57.28 78.79 | 35.88 Total | 278 538 213 33 | 1,062 | 100.00 100.00 100.00 100.00 | 100.00 Kendall's tau-b = 0.3511 ASE = 0.026

In other words, how do we find out that it is the ONLY reason? Intervening relationship A causes B which causes C. A causes C because it causes B which then causes C. So, now what do we need to do to see if political interest has an effect on participation BECAUSE it causes self efficacy? In other words, how do we find out that it is the ONLY reason?

Political interest and participation when self efficacy is high | How much interest do you have in political polpartbes | affairs c | No intere Not very A fair am A great d | Total -----------+--------------------------------------------+---------- 0 | 107 184 52 3 | 346 | 56.61 50.55 28.57 9.68 | 45.17 1 | 25 60 21 2 | 108 | 13.23 16.48 11.54 6.45 | 14.10 2 | 57 120 109 26 | 312 | 30.16 32.97 59.89 83.87 | 40.73 Total | 189 364 182 31 | 766 | 100.00 100.00 100.00 100.00 | 100.00 Kendall's tau-b = 0.1728 ASE = 0.031

Political interest and participation when self efficacy is low | How much interest do you have in political polpartbes | affairs c | No intere Not very A fair am A great d | Total -----------+--------------------------------------------+---------- 0 | 67 103 9 1 | 180 | 75.28 59.20 29.03 50.00 | 60.81 1 | 15 22 9 1 | 47 | 16.85 12.64 29.03 50.00 | 15.88 2 | 7 49 13 0 | 69 | 7.87 28.16 41.94 0.00 | 23.31 Total | 89 174 31 2 | 296 | 100.00 100.00 100.00 100.00 | 100.00 Kendall's tau-b = 0.1460 ASE = 0.046

So, does controlling for political interest mitigate the effect of self efficacy?

Self efficacy and participation when political interest is medium | Compared to most political leaders, how much better or polpartbes | worse could you personall c | Much wors Somewhat Equally Somewhat Much bett | Total -----------+-------------------------------------------------------+---------- 0 | 87 83 55 18 5 | 248 | 69.60 60.14 54.46 42.86 33.33 | 58.91 1 | 25 12 9 2 2 | 50 | 20.00 8.70 8.91 4.76 13.33 | 11.88 2 | 13 43 37 22 8 | 123 | 10.40 31.16 36.63 52.38 53.33 | 29.22 Total | 125 138 101 42 15 | 421 | 100.00 100.00 100.00 100.00 100.00 | 100.00 Kendall's tau-b = 0.2554 ASE = 0.040

Self efficacy and participation when political interest is high | Compared to most political leaders, how much better or polpartbes | worse could you personall c | Much wors Somewhat Equally Somewhat Much bett | Total -----------+-------------------------------------------------------+---------- 0 | 6 8 28 4 4 | 50 | 33.33 42.11 46.67 5.80 11.76 | 25.00 1 | 4 6 13 5 1 | 29 | 22.22 31.58 21.67 7.25 2.94 | 14.50 2 | 8 5 19 60 29 | 121 | 44.44 26.32 31.67 86.96 85.29 | 60.50 Total | 18 19 60 69 34 | 200 | 100.00 100.00 100.00 100.00 100.00 | 100.00 Kendall's tau-b = 0.3995 ASE = 0.053