This document summarizes all test material for the midterm exam of ARMS. Some parts of the Grasple lessons are written in Dutch, but overall in English.
With this summary i got an 8 for the exam.
,Lecture 1 Multiple Linear Regression (MLR)
Frequentist framework = tests how well the data fits the null hypothesis (NHST)
- P-values
- Confidence intervals (=if we were to repeat this experiment many times and calculate
a CI each time, 95% of the intervals will include the true parameter value, and 5%
won’t)
- Effect sizes
- Power analysis
Bayesian framework = probability of the hypothesis given the data, taking prior information
into account
- Bayes factor (BFs)
- Priors (expectation beforehand)
- Posteriors (=prior and data)
- Credible intervals (=there is 95% probability that the true values is in the interval)
Empirical research = uses collected data to learn from, information is captured in a likelihood
function. →frequentist
X-axis: values for population mean
→for example height: 140 and 230 cm height for an adult are less likely than 165 cm for an
adult.
Y-axis: probability of the observed data for each value of population mean (µ)
Bayesian approach = prior knowledge is updated with information in the data and together
provides the posterior distribution for µ
- Advantage = accumulating knowledge (today’s posterior is tomorrow’s prior)
- Disadvantage = results depend on choice of prior
The posterior distribution of the parameters of interest provides all desired estimates:
- Posterior mean or mode
- Posterior SD (comparable to frequentist standard error)
- Posterior 95% credible interval (providing the bounds of the part of the posterior in
which 95% of the posterior mass is)
Results depend on things not observed and on the sampling plan (how you test).
Bayesian probability = probability that hypothesis Hj is supported by the data.
→Pr(Hj|data)
Frequentist probability = probability of observing same or more extreme data given that the
null hypothesis is true (p-values).
→Pr(data|H0)
PMP = Posterior Model Probability; the (Bayesian) probability of the hypothesis after
observing the data
→are also relative probabilities
, →PMPs are updates of prior probabilities for hypotheses with the BF
Bayesian probability of a hypothesis being true depends on two criteria:
- The prior = how sensible it is, based on prior knowledge
- The data = how well it fits the new evidence
Bayesian testing is comparative: hypotheses are tested against one another
Bayes Factor (BF) = 10 → support for H1 is 10 times stronger than for H0
Bayes Factor (BF) = 1 → support for H1 is as strong as support for H0
Both frameworks use probability theory, but:
- Frequentist: probability is the relative frequency of events
→more formal
- Bayesian: probability is the degree of belief
→more intuitive
→this leads to debate (=same word is used for different things)
→and leads to differences in the correct interpretation of statistical results (like confidence
and credible interval)
Multiple linear regression (MLR)
‘normal’ linear regression:
^Y = B0 + B1 x X
^Y = intercept + slobe x X-value
→so we use X to predict Y
Residual = distance from the line = e
Multiple linear regression = with more predictors (Y = observed, Y^ = predicted)
Y = B0 + B1 x X + B2 x X + e
Y = intercept + slobe 1 x X-value + slobe 2 x X-value + residual
→Life satisfaction decreases by age, but increases by years of education
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller nicolejdikkeboer. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $12.65. You're not tied to anything after your purchase.
