A simple Markov Chain Monte Carlo example

 RPubs - A simple Markov Chain Monte Carlo

Kernel regression for non-linear relationship

 RPubs - Kernel regression

Using Bayesian linear regression to predict

 RPubs - Bayesian linear regression

loggamma distribution

 RPubs - loggamma distribution

General format of mixture distribution

 RPubs - General format of mixture distribution

Note for proving Student's theorem

 RPubs - Notes for student's theorem

Notes for Student t distribution

https://rpubs.com/enwuliu/983191

Calculations for random effect model meta-analyisis

 RPubs - Random effect meta-analysis

Variance of mixture normal distribution

 RPubs - Variance of mixture normal distributions

RPubs - General format of mixture distribution

Noncollapsibility, confounding, and sparse-data bias.

 Part 1:

Noncollapsibility, confounding, and sparse-data bias. Part 1: The oddities of odds - Journal of Clinical Epidemiology (jclinepi.com)

Part 2:

Noncollapsibility, confounding, and sparse-data bias. Part 2: What should researchers make of persistent controversies about the odds ratio? - Journal of Clinical Epidemiology (jclinepi.com)

generalized linear model - Is there a mathematical definition of non-collapsibility? - Cross Validated (stackexchange.com)

Estimating and contextualizing the attenuation of odds ratios due to non collapsibility: Communications in Statistics - Theory and Methods: Vol 46, No 2 (tandfonline.com)

Joint cumulative distribution of X1 and X2

 

Proving law of the unconscious statistician (LOTUS) for discrete variable

 

Multiple conditions

From 

https://jonathanweisberg.org/vip/multiple-conditions.html#multiple-conditions

 9 Multiple Conditions | Odds & Ends (jonathanweisberg.org)

When to Adjust Alpha During Multiple Testing

https://www.qeios.com/read/QIH0Q1

When to Adjust Alpha During Multiple Testing - Article (v1) by Mark Rubin | Qeios

Counting number of duplicated cases by several variables

proc sort data=have(keep=key1 key2);
  by key1 key2;
run;
data want;
  do count=1 by 1 until(last.key2);
    set have;
    by key1 key2;
    end;
run;

A very clear introduction to B-SPLINES

 

MLE and REML in mixed models

 In mixed models, if use MLE, we have to assume that fixed effects are known, rather than being estimated from the data.  If we use REML (residual maximum likelihood) it will automatically adjust for the degree of freedom corresponding to estimated fixed effects. This is the key difference between MLE and REML in mixed models,   however, the difference will be very small when the sample size is big.