Summary: Advanced Statistics

Read the summary and the most important questions on Advanced statistics

• 1 Cross-sectional data (MLM)

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• 1.1 MLM Part 1 mixed effects: random intercept & linear

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• What does the var (_cons) mean in the random part of the model?

  This is the variance over the intercept. You dont really use this number, because you only present the fixed effect coefficients, but you have to take clustering into account.

• What does log liklihood say?

  The likelihood itself doesnt really have an interpretation. You can perform the -2 log likelihood test with 2 models to determine the best model.

• What is the interclass correlation coefficient (ICC)?

  A way of showing how important the adjustment is. 
  you could give the likelihood ratio test but its not very informative. 
  ICC gives the magnitude of the average correlation that you find within the neighbourhood (within the cluster variable)
  between group variance (variance over the intercept) / total variance

• What is the formula for ICC?

  ICC = between group variance over the intercept. var(_cons) / var(_cons) + residual

• What does this var (residual) mean?

  This is the unexplained variance left after grouping by this grouping variable. This is the little epsilons left that go from the individual observation to the regression line.

• 1.2 MLM Part 2 random slope & logistic

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• What does it mean that the intercept and slope are often correlated to eachother?

  When you start high with an intercept, you often see that the slope is more steep compared to the lowest intercept, (positive magnitude)
  or
  that the slope is less steep compared to the lowest intercept (negative magnitude)

• What is covariance and why do you need to add it?

  This says something about the correlaiton between the slope and the intercept. You have to add this when you add a random slope to your model, because then you can tell something about the correlation between the random slope and intercept. 
  negative number means high intercept less steep - low intercept more steep
  positive number means high intercept more steep - low intercept less steep

• How can you decide wether you need a random intercept or slope

  Intercept: -2 log likelihood ratio test compared to naive model
  Slope: -2 log likelihood ratio test compared to model with random intercept

• Why do you often not need a random slope for logistic regression model? What is better to do?

  Often stata will give error. Its hard to imagine different slopes for binary outcome, the curve gives probabilities.
  its better to model the interaction term in the fixed part of the model (when there are not too many categories)

• 1.3 MLM Part 3

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• How can you use variance as explanation? (4 steps)

  1. Have an intercept only model. So have a model with 1 outcome and a cluster variable.
  2. Write down the variance over the intercept var(_cons) of the intercept only model.
  3. Add in the fixed part the variable
  4. Write down the new variance over the intercept var(_cons).
  
  compare the two variances with each other.