# maximum likehood

1. ### Testing Model Fit between Subsets of Data When Using Multilevel Models

When using multilevel models based on maximum likelihoods, one can use either deviance statistics (e.g., -2LLs) for nested models or information criteria (e.g., Bayesian Information Criterion, BIC) to test which of two models better fit the data--as long as the models are both used to fit the...
2. ### Difference between VCV by inverting Hessian at ML and by Hierarchical Bayes

Let's say we have a multimomial logit problem and we find the best beta coeffcients b* aggregating all units. The inverse of the Hessian at b* gives us a VCV matrix at this point which shows roughly how betas vary across units. The other way to get a VCV matrix is to use Hierarchical Bayes where...
3. ### MLE or instrumental variables

I'm trying to estimate a model in which one of the explanatory variables is correlated with the error term. As I see it there are two alternatives, specify the likelihood function and maximize it to get the estimates of the coefficients, or use instrumental variables. There are pros and cons...
4. ### Five Category Ordered Probit Log Likelihood Function in R Help : Survey Data Research

I am currently working with some survey data that has a 5 category scale. I have used a ML method before for a 4 category scale and I am trying to adapt the code for the new survey in R. The original code that worked was: #Load Data mathcomp <- read.csv("RRawComposite11.csv"...
5. ### Proof of asymptotic normality of MLE

If someone has seen these theorems I would appreciate some help in understanding a part of a certain proof. The usual way to show that \sqrt{n} \left( \hat{\theta}-\theta_0 \right) \xrightarrow{D} N \left( 0, \frac{1}{I \left( \theta_0 \right)} \right) is to expand l \prime \left( \theta...
6. ### Proof of constistency of Maximum Likelihood Estimators (MLE)

Hi all, I would appreciate some help comprehending a logical step in the proof below about the consistency of MLE. It comes directly from Introduction to Mathematical Statistics by Hogg and Craig and it is slightly different than the standard intuitive one that makes use of the Weak Law of...
7. ### Regression Poisson

Hi :wave:, first of all, sorry for my english, I'm not english. My question is a quite specific of a problem. I'm doing a regression of a Poisson distribution, log(\beta)=\alpha+\beta x where x=0 to a placebo study and x=1 otherwise. Also I considere the effect \delta = \frac{\mu_A}{\mu_P}...
8. ### how to test for significant differencecs in ML estimates after optim()

I am trying to test whether or not there is a significant difference between maximum likelihood estimates of two genetic parameters (selection and dominance) across two environments with genotype data from a cross. There are three genotype classes, C11, C12, and C22, and I am looking to maximize...
9. ### Fitting a model with Bernoulli/Binomially distributed data

I am used to fitting data to estimate parameters in a model f(x,A) where x is my data point and A is the parameter(s) to be determined. To achieve this I usually use chi-squared fitting, so I am minimizing \chi^2 = \sum \frac{(y_i - f(x_i,A))^2}{\sigma_i^2}. I have recently been given an almost...
10. ### Manual

Hi guys, I'm a geologist and I'm looking for a good manual to learn about with power law distribution and maximum likehood (beginner-medium level). My goal is to write a code to define the best straight line between an upper and lower bound in log-normal (fractal dimension) Thank you...