Psychology 290 Special Topics Study Course: Advanced Meta-analysis

1. Psychology 290Special Topics Study Course: Advanced Meta-analysis March 10, 2014

2. The plan for today • Wrap up likelihood ratio test from last time. • How to get standard errors for estimated conditional means. • A much more complex example.

3. Getting standard errors • When we have separate groups that have both a common mean and a common variance component, we can get the standard error using a separate weighted analysis. • However, the model will not always be so simple. • We can get standard errors • From the Hessian matrix; • From regression output.

4. Using the covariance matrix • In general, in any statistical package, it will be possible to obtain the covariance matrix of the parameter estimates. • In R, this is obtained by the command “vcov(regout)” (where regout is output from the lm() function). • The variance of a conditional mean may be calculated from the regression coefficients and the covariance matrix.

5. The covariance matrix (cont.) • The formula for the variance of a linear combination of the form Y = a + b1X1 + … + bkXkis:

6. The covariance matrix (cont.) • In regression, that is where standard errors of predicted means come from. • In meta-analysis, there is an additional complication: the covariance matrix is too large by a factor of MSe. • (Demonstration in R.)

7. Continuing the vc-model example • The Insko lab effect: a much more complex example.

8. Next time… • Next week, funnel plot asymmetry and publication bias.