Consistency in parameter labels

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tbates's picture
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Joined: 07/31/2009

The regression example (2.1.1 Simple Regression)

states y = β0 + β 1 ∗ x + ϵ

Then in the text below the parameters are called " β0 , β1 , σ2, ϵ , and the mean and variance of x".

And then in the diagram we see σ2x2y, βy, βyz and μx.

Much easier to follow with one set of conventions rather than three. And where mapping of conventions is necessary, it should be explicit (i.e., "and the mean and variance of x (μx and σ2x respectively) )"

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Steve's picture
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Joined: 07/30/2009
Nice flow. I like it. I

Nice flow. I like it.

I wonder how we should treat these kinds of edits. It might be nice if we started a set of documentation as wiki pages so we could be working in parallel on them.

tbates's picture
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Joined: 07/31/2009
Can that be made to happen?

Can that be made to happen?

Would be a very good idea at this early stage, I think

tbates's picture
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Joined: 07/31/2009
PS: I would add a helper

PS: I would add a helper equation there along the lines of "In regression we are finding the line that best relates our dependent variable (Y) to the independent variable (X), so we will typically want to know both the slope (how much Y increases for each increment in X) and possibly the intercept as well (how much Y we have even when X is 0). This is traditionally expressed as Y = b*X + C

In the conventions of statisticians, the intercept is termed βo, the slope β1. In SEM, we also model the error (epsilon: ϵ) inherent in our measurement of x, giving us:

y = β0 + β 1 ∗ x + ϵ

In R you may be used to running this as

  data(myRegData)
  myModel = lm(y~x, data= myRegData); 
  anova(myModel)

Here we will implement this in OpenMx...