faAantekeningen ARMS
HC1:
All Emails to
Second part to
Two frameworks:
Frequentist framework: still mainstream, based on H0, p-values (what is the probability of h0
being true but finding something else), confidence intervals,, effect sizes and power analysis
- All relevant information for inference is contained in the likelihood function
Bayesian framework: Increased attention because of replication crisis
- Prior knowledge is updated with information in the data and together provides
posterior distribution for Mu
o Advantage is accumulating knowledge
o Disadvantage results depend on choice of prior
Combining prior and data makes posterior
- Prior can be useful for posterior distribution
o Posterior mean or mode: the mean or mode of the posterior distribution
o Posterior SD: SD of posterior distribution (comparable to frequentist standard
error; uncertainty in estimate)
o Posterior 95% credible interval: Providing the bounds of the part of the
posterior in which 95% of the posterior mass is (not confidence but credible
interval)
There are 5 priors:
- No information
- An average score will be definitely be between these limits (flat)
- Normal distribution
- Very specific (trusting prior knowledge)
- Very specific for subpopulation (really low or really high; very unrealistic)
Both are empirical research. Information in both data is captured in a likelihood function.
Maximum likelihood estimate is also based on a likelihood function.
Bayes conditions on observed data; whereas frequentist testing conditions on H0
- (Bayes) Probability that hypothesis is supported by the data
- (Frequentist) P-value probability of observing same or more extreme data given that
the null is true
Researchers with hypotheses may prefer to get information on the probability that their
hypotheses are true, to what extent does the data support their hypotheses?
- PMP = posterior model probability
o The Bayesian probability of the hypothesis after observing the data
Two criteria
, - How sensible it is, based on current knowledge (the prior)
- How well it fits new evidence (the data)
Bayesian testing is comparative; hypotheses are tested afainst one another
1 is the turning point
- >1 is more for H1
- <1 is more for H0
Both frameworks use probability theory:
- Frequentist is relative to frequency (formal)
- Bayes is relative to degree of belief (intuitive)
Also leads to debate
Confidence interval: If we were to repeat this experiment many times and calculate a CI each
time, 95% if the intervals will include the true parameter value
Credible interval: There is 95% probability that the true value is in the credible interval
FOMO article uses MLR (multiple linear regression analysis) and hierarchal linear regression
- Does FoMo add to the prediction of ISA on top of all other predictors
Least squares principle, the distance between each observation and the model is as small as
possible.
With multiple linear regression model
Y = B + ax + cx +dx + e
B= intercept
X = slope
E = residual (normally distributed with mean 0)
Observed outcome is prediction based on the model and some error in prediction
Model assumptions:
- All results are only reliable if assumptions made by the model and roughly hold
o Serious violations lead to incorrect results
o Sometimes there are easy solutions (outlier or quadratic term) and
sometimes not
o Per model, know what assumptions there are and always check them
carefully (grasple lesson)
- MLR assumes interval/ratio variables (outcome and predictors)
Dummy coding for categorical values (gender):
- Recode to 1 and 0
- Interpretation: difference in mean grade between males and females (with the same
age)
- More on grasple
, For evaluating the model:
- With frequentist statistics:
o Estimates
o Test with NHST if parameters are significantly non-zero
R2 = correlation between observed and predicted Y (explained by
model; value for sample)
H0 = 0 and H1 >0
Adjusted R2 = Doesn’t use sample but population estimate (Corrects
for overfitting and non-significant predictors)
Beta = X to the prediction of Y (Unique contribution; If people have the
same age, then what is the contribution of education)
H0 = 0 and H1=/0
Unstandardized coefficient used for y= ax +b
Standardized coefficient is for normal distribution and can be used for
comparison
- Bayes
o Estimate parameters of model
o Compare support in data for different models/ hypotheses using bayes factors
Null model is model with Bage = 0 and Beduc =0
Model1: age+educ includes the predictors without constraints
BF10 = 28.181 so a lot for model 1 compared to model 0
Bayesian estimates are summary of posterior distribution of
parameters B
BFinclusion evaluates if the model improves with this predictor
Hierarchal linear regression analysis: comparing 2 nested models
- Are both predictors useful together for prediction of variable?
o R2 change
o Unstandardized B changes with model
Research can be exploration or theory evaluation
Frequentist:
- Method enter (Theory evaluation): data analyst decides what goes in the model
- Method stepwise(Exploratory): the best prediction model is determined based on
results in this sample
o Which method capitalizes most on chance? Stepwise
o Which method has best chance to get replicated? Enter
Bayes:
- As implemented in JASP-base: some what exploratory
- BAIN can evaluate informative hypotheses -> confirmatory
Grasple week 1:
HC1:
All Emails to
Second part to
Two frameworks:
Frequentist framework: still mainstream, based on H0, p-values (what is the probability of h0
being true but finding something else), confidence intervals,, effect sizes and power analysis
- All relevant information for inference is contained in the likelihood function
Bayesian framework: Increased attention because of replication crisis
- Prior knowledge is updated with information in the data and together provides
posterior distribution for Mu
o Advantage is accumulating knowledge
o Disadvantage results depend on choice of prior
Combining prior and data makes posterior
- Prior can be useful for posterior distribution
o Posterior mean or mode: the mean or mode of the posterior distribution
o Posterior SD: SD of posterior distribution (comparable to frequentist standard
error; uncertainty in estimate)
o Posterior 95% credible interval: Providing the bounds of the part of the
posterior in which 95% of the posterior mass is (not confidence but credible
interval)
There are 5 priors:
- No information
- An average score will be definitely be between these limits (flat)
- Normal distribution
- Very specific (trusting prior knowledge)
- Very specific for subpopulation (really low or really high; very unrealistic)
Both are empirical research. Information in both data is captured in a likelihood function.
Maximum likelihood estimate is also based on a likelihood function.
Bayes conditions on observed data; whereas frequentist testing conditions on H0
- (Bayes) Probability that hypothesis is supported by the data
- (Frequentist) P-value probability of observing same or more extreme data given that
the null is true
Researchers with hypotheses may prefer to get information on the probability that their
hypotheses are true, to what extent does the data support their hypotheses?
- PMP = posterior model probability
o The Bayesian probability of the hypothesis after observing the data
Two criteria
, - How sensible it is, based on current knowledge (the prior)
- How well it fits new evidence (the data)
Bayesian testing is comparative; hypotheses are tested afainst one another
1 is the turning point
- >1 is more for H1
- <1 is more for H0
Both frameworks use probability theory:
- Frequentist is relative to frequency (formal)
- Bayes is relative to degree of belief (intuitive)
Also leads to debate
Confidence interval: If we were to repeat this experiment many times and calculate a CI each
time, 95% if the intervals will include the true parameter value
Credible interval: There is 95% probability that the true value is in the credible interval
FOMO article uses MLR (multiple linear regression analysis) and hierarchal linear regression
- Does FoMo add to the prediction of ISA on top of all other predictors
Least squares principle, the distance between each observation and the model is as small as
possible.
With multiple linear regression model
Y = B + ax + cx +dx + e
B= intercept
X = slope
E = residual (normally distributed with mean 0)
Observed outcome is prediction based on the model and some error in prediction
Model assumptions:
- All results are only reliable if assumptions made by the model and roughly hold
o Serious violations lead to incorrect results
o Sometimes there are easy solutions (outlier or quadratic term) and
sometimes not
o Per model, know what assumptions there are and always check them
carefully (grasple lesson)
- MLR assumes interval/ratio variables (outcome and predictors)
Dummy coding for categorical values (gender):
- Recode to 1 and 0
- Interpretation: difference in mean grade between males and females (with the same
age)
- More on grasple
, For evaluating the model:
- With frequentist statistics:
o Estimates
o Test with NHST if parameters are significantly non-zero
R2 = correlation between observed and predicted Y (explained by
model; value for sample)
H0 = 0 and H1 >0
Adjusted R2 = Doesn’t use sample but population estimate (Corrects
for overfitting and non-significant predictors)
Beta = X to the prediction of Y (Unique contribution; If people have the
same age, then what is the contribution of education)
H0 = 0 and H1=/0
Unstandardized coefficient used for y= ax +b
Standardized coefficient is for normal distribution and can be used for
comparison
- Bayes
o Estimate parameters of model
o Compare support in data for different models/ hypotheses using bayes factors
Null model is model with Bage = 0 and Beduc =0
Model1: age+educ includes the predictors without constraints
BF10 = 28.181 so a lot for model 1 compared to model 0
Bayesian estimates are summary of posterior distribution of
parameters B
BFinclusion evaluates if the model improves with this predictor
Hierarchal linear regression analysis: comparing 2 nested models
- Are both predictors useful together for prediction of variable?
o R2 change
o Unstandardized B changes with model
Research can be exploration or theory evaluation
Frequentist:
- Method enter (Theory evaluation): data analyst decides what goes in the model
- Method stepwise(Exploratory): the best prediction model is determined based on
results in this sample
o Which method capitalizes most on chance? Stepwise
o Which method has best chance to get replicated? Enter
Bayes:
- As implemented in JASP-base: some what exploratory
- BAIN can evaluate informative hypotheses -> confirmatory
Grasple week 1:
