OLS regression, student level: Math achievement on liking math and cultural values

Here’s a description of the project I’m working on.

I duplicated all country-level variables to student level, then ran a student level regression of math on liking for math (PATM), per capita GDP (GDP), and cultural value indexes (Rational and Self Expressive).

Collinearity was not too high — all variance inflation factors were less than 3.

Coefficientsa
Model Unstandardized Coefficients Standardized Coefficients t Sig.
B Std. Error Beta
(Constant) 382.428 .586 652.822 .000
PATM 4.969 .066 .163 75.521 .000
GDP 4.787 .027 .592 175.670 .000
Rational 23.244 .249 .235 93.291 .000
Self Expressive -33.841 .279 -.361 -121.273 .000
a. Dependent Variable: Math

These are all as I expected.

  • The more a student likes math, the better she does (this is a reciprocal relationship because if you do better at math, you like it better too)
  • Higher GDP is associated with higher math achievement
  • Higher secular rational values are associated with higher math achievement; in other words, traditional values are associated with lower math achievement
  • Higher self expressive values are associated with lower math achievement

The residuals looked fairly normal, though there were more positive ones than negative ones.This could represent an omitted variable (perhaps extrinsic valuing of math? which I could calculate from some other TIMSS questionnaire items) or some nonlinearity in the relationship.

The model has an R square of .321.

Now I’m ready to start running HLM analyses to see if countries with higher rationality and lower self expressiveness offer higher “returns” to liking math.

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4 responses to “OLS regression, student level: Math achievement on liking math and cultural values

  1. make me feel better by checking for multicollinearity…

  2. never mind I re-read it and you did it.
    I’m still bothered by the “Rational/Math/GDP” entanglement. That just feels like a mediated relationship.

    I have to be rational to appreciate math. particularly higher math. Rationality tends to favor science, science tends towards technology, technology tends towards affluence/GDP…

    GDP is stomping the rest of the variables for influence, so I think that turns into a feedback loop. Once I have technology, I really need techs. Techs need math.

    I wonder if the “self-expressive” variable might be pointing at left-brain/right-brain differences.
    Developing artists instead of mathematicians.

    I’d also tend to believe the top 10% of GDP would show a flatter relationship (resting on their laurels). Just an idea.

    Because you’re trying to draw out the influence of liking, I’d probably group GDP and see what you get within groups.

    Anyway I hope some of that helps.

  3. well actually the collinearity is a concern, the VIFs were over 2.5 for some predictors. But I have a lot of data and anyway the OLS is just a step on the way to the HLM.

    Maybe I need to do an SEM — good, have next quarter’s project ready. There are plenty of endogenous variables here.

    The self-expressive variable is at the country level. Can an entire country be right-brained?

    There is definitely a flattening out of math achievement at higher levels of GDP.

    Thanks for coming by! Almost like having you sitting next to me in class. :)

  4. One other thing, GDP actually isn’t the only influential variable. Once you control for it, secular-rational and self-expressive values are still important in determining the intercept of math achievement (higher sec-rational means higher math achievement, lower self-expressive means higher math too).

    And this is what is really cool… countries with higher self-expressive values have lower slopes for the math achievement on liking-math regression. That’s what I was looking for. But it is a faint effect, not sure if because of the weird distributions of liking math in some countries or just not that important.

    But still there’s all that entangling/mediation of variables. Not really sure what to think or do about that.