Questions tagged [wald-test]

Hypothesis test based on the approximate normal distribution of the maximum likelihood estimator.

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F-test and Wald test in time series

Assume we have the time series $X_{1,t}$ and $X_{2,t}$ where $X_{i,t}=(x_{i,1},...,x_{i,T})$. We build two models as (Assume the time series are weakly stationary): \begin{align} X_{1,t}=\sum_{\...
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How does the following term happen when using the Wald Test on two-sample binomials?

I'm having trouble understanding one of the steps of the Wald test used in two-sample binomial proportions. More specifically, when $X_1, ..., X_{n_1}$ are iid Binomial$(1, p_1$), $Y_1, ..., Y_{n_2}$ ...
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Type II vs. Type III using car::Anova on lmer model [duplicate]

I have fit a linear mixed-effects model using lmer. The model includes 1 categorical predictor variable, 2 continuous predictor variable, all interactions, and a categorical random effect. To test for ...
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Wald test for Cox PH coefficients: Z distributed

I'm wondering about the Wald test when applied to regression coefficients in the Cox PH model. In linear regression, you have to estimate $\sigma^2$ separately from the mean, which means the standard ...
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Regarding the type 2 or 3 ANOVA, does the analysis via model reduction correspond to LRT and via contrasts - to Wald approach?

I noticed, that in R we can obtain type 2 and type 3 ANOVA in many ways in unbalanced designs: For example, for type-2 car::Anova(...type=2), by running anova() over a sequence of models with swapped ...
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How to get the $95\%$ Wald test confidence interval for $\theta$? [closed]

Suppose that iid random samples $X_i$ from a discrete CDF $F(x)$ on $\{x_1,\dots, x_n\}$ with mean $EX=\theta$. We want to estimate $F(x)$. We consider empirical likelihood for $F(x)=\sum_{i=1}^n p_i ...
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Likelihood-based CI is better than Wald CI?

The text I'm reading mentions the following: Let us consider a scalar parameter case. The likelihood-based approximate 95% cI is $$\left\{\theta,2\log\frac{L(\hat{\theta})}{L(\theta)} \le3.84 \right\}$...
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When is the z-score/wald-score results will be a non-normal distribution?

If the hypothesis is valid the distribution of scores from several samples from the same population will follow a normal distribution for the z-test. That is true? I've made a simple experiment to see ...
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Does values standardization affect its distrution?

I have Wald's test results from comparing sensitivity and specificity of LDA and QDA. Results are almost the same. I generate data, train and classify it and then obtain the Wald statistic. I need to ...
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Derivation of Distribution for the Robust F-statistic

This question is motivated by the question here. That question asked about the formula for a robust F-statistic. I am aware of the formula. My question is how to prove the distribution of the test ...
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Wald test for sum of coefficients in R

I am "translating" code from STATA to R, and need to translate the following command: ...
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Distribution of the F-statistic of a Wald test

On the Wikipedia page for the Wald test, there is a derivation for the test statistic under multiple hypotheses. The derivation ends in an F-distribution. I am curious about the final step in that ...
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Can we report an F statistic on a Robust Linear Model with only Fixed Effects?

I'm estimating a fixed effects model using Linear Regression with the Huber weighting function. I included a boxplot of the data. How do we report an F-value and significance for the entire model like ...
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Does modelling higher order interaction terms meaningfully affect type II tests of lower order terms?

My understanding of type II testing is that you compare a model with each tested factor, and all equivalent or lower-order terms, with a model excluding that factor. For example for y ~ a+b + ab, a ...
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Why is the p-value given by p-value${}=P(\chi^2>\Delta D)$ rather than p-value${}=2P(\chi^2>\Delta D)$ as $(*)$?

In the Binomial Regression Models for Binary Data, we have the general Wald statistics result for the Hypothesis $H_0: \beta_j=0, \, H_a: \beta_j \neq 0$ that the p-value is given by $$\text{p-value}=...
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Are there small-sample cases where we can approximate the distribution of the Wald statistic better than with the Normal/Chi-squared distribution?

In my specific case, I'm referring to the parameter estimates of a binomial regression (regardless of whether we are estimating risk ratios or odds ratios). Can the problem of divergence of the Wald ...
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Logistic regression multivariate : Odds ratio / Wald-test

I have a small problem with one of my analyses. I'm doing a multivariate logistic regression so some continuous variables have been discredited by quartiles. Here are my results: OR and IC Variable ...
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Why is it hard to do a one-sided Wald test for multiple linear hypotheses?

I've heard that one can't do a one-sided Wald test for multiple linear hypotheses, and I found that a Stata FAQ page wrote: ... The "test" command can perform Wald tests for simple and ...
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How to build a saturated model for logistic regression in R?

I want to build a saturated model in R for my logistic regression. I already tried the following code obtained from another question posted here (Logistic Regression : How to obtain a saturated model):...
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Difference-in-differences on compliers

I'm trying to estimate a generalized DID (two periods three groups)'s local average treatment effect on Stata. The DID code used was: ...
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How to get adjusted logrank in the Cox model, if I have two covatiates?

Let's say I have a model (pseudolanguage): survival = My_Factor + sex + age. I do it to adjust the hazard ratio for sex and categorized age={<30yr; >=30yrs} (not my choice). I can get two p-...
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Weighted Survey Data Comparison of Many Group Means

We have a state representative sample of student data that must be analyzed using survey weights. What I am struggling with, conceptually, is what comparisons are actually possible under this design. ...
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What measure to use to compare stratified and non stratified Cox proportional hazards in R

I am doing past papers studying for an exam on medical statistics and am unsure about one of the questions. The question reads as follows: "Consider now a second model where we stratify by sex ...
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Multivariate Granger Test on Single Variables

Say I have some trivariate model with variables X, Y, Z. Now I want to know if X granger causes Y. To do this test I have used the causality() function in ...
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correlation between dependent variable and instrument

I have an additional question to the issue of correlation between dependent variables and instruments - which i have some problems understanding. I'm estimating a model by IV due to endogeneity in a ...
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Why use the Wald test in logistic regression?

Some statistical software use the Wald statistic when reporting on the regression coefficients. As examples, R and Stata report Wald by default. The logistic regression article on Wikipedia says, ...
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I only need to know these two tests

Just a quick sanity check, if a want to do an hypothesis testing about the mean, following the Central Limit theorem the sampling distribution of the mean is asymptotically normal, then the only tests ...
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Hypothesis testing after bootstrap

I have a revenue measure over 2 distinct groups of users (group A and B in an A/B test), but the revenue distribution across users is definitely not Normal. In order to measure a random variable that ...
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Wald F test vs Wald T test

What is the difference between the Wald F test and Wald T test? I understand one uses the T distribution and the other an F distribution but I am unsure in which situations one is appropriate and the ...
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Wald Test with one-sided alternative hypothesis

it is not clear to me what happens if I want to use the Wald test to test a simple hypothesis vs a one-sided alternative. I know that if I have $H_0: \theta = \theta_0$ vs $H_1: \theta \neq \theta_0$, ...
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Comparing coefficient across groups in 3 way linear mixed model

I wonder how to compare coefficients across group in linear mixed model. Dependent variable (DV, continuous variable) is changed by time variable (T, continuous, fixed effect). And hypothesis is that ...
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Wald Statistic Simplification - 2 Restrictions?

(Specify the wald statistic as: W=$(R\hat{\theta}-r)'[R\hat{V}(\hat{\theta})R']^{-1}(R\hat{\theta}-r)$ Where r is a vector of restrictions, R imposes the restrictions on $\hat{\beta}$, $\hat{\theta}$ ...
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Asymptotic equivalence of Likelihood Ratio Statistic and Wald Statistic?

When we say the likelihood ratio statistic and the Wald statistic of a set of binomial distributions are asymptotically equivalent, do we mean that the sampling distributions of the two statistics ...
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ARDL model: Is it valid the use of Wald test on short-run coefficients to determine causality?

I estimated an ARDL model and there was cointegration based on bound tests. I obtained the error correction form. Most journal articles I have seen assess sort-run causality by just performing Granger ...
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Testing linear hypothesis with Wald test: unintuitive results

I have a question about testing the equivalence of two regression parameters. I know there are a lot of resources about how to test a linear hypothesis but I am confused about my results (and its been ...
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Why should one do Wald test after linear regression

I see that the Wald test can be performed on the model obtained from linear regression as shown here. I understand that it gives information whether a predictor is adding significant value to outcome ...
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Test hypothesis of the probabilities being the same using using Wald test statistic [closed]

I am trying to understand how to use the Wald test to test the hypothesis that the probabilities of getting a faulty product are the same in two samples. The whole text of a task is: Two factories ...
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Why did I get inconsistent result from ANOVA and wald test

I tested the effect of one factor X on my response Y. The factor has four levels A, B, C, and D and the null hypothesis I want to test is A=B=C=D. ...
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How can these two expressions both converge in distribution to N(0, 1)?

In All of Statistics, chapter 11 (pg. 183), Larry Wasserman states in his description of the Wald Test: We are testing the null hypothesis $ \hat{\theta} = \theta_0 $ versus the alternative ...
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Logistic regression Wald statistic

I have to do a logistic regression analysis. I'm attempting to understand which variables I am taking out of a model. I am doing a simple hypothesis test to understand whether I should keep an ...
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How do I check the assumptions of the Wald test for binomial GLM?

At my statistics course we used LRT to get the p-value of the covariates from a binomial GLM. There was something mentioned about the Wald test assumptions not being met, which results in biased p-...
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Hypothesis Test for a Linear Combination of Three or More Probabilities

Suppose that you have a parameter w. As you change the value of that parameter, the probability of a given event occurring increases or decreases. I want to use the Method of Finite Differences to ...
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Meta-analyzing Likehood ratio or wald test outputs

Hope your day is going well! I've been reading a lot on the Wald test and likelihood ratio test recently because it is the output of my RNA sequencing data. I was interested in meta-analysis of ...
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Likelihood ratio, Wald, and Score are equivalent?

In Foundations of Linear and Generalized Linear Models, Agresti makes a comment on page 131 about likelihood ratio, Wald, and Score testing of regression parameters. For the best-known GLM, the ...
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Is Wald Z test two tailed?

I would like to ask you whether the Wald Z test which is used in context of null model for multilevel logistic regression is actually two-tailed or not. So far, I've found that Wald has chi-square ...
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Difference between Wald test and Chi-squared test

I am aware that both tests assume Chi-square distribution of data. Here are what I know: Wald test as multi-variable generalization of student's t-test tests the statistical difference of mean ...
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Is it possible to generate power curves for score-tests, wald-test, LR test?

A power curve is something in the example Do score-tests, wald-test, LR test have power curves? What do they look like?
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Where are the Wald p-values and where are the LRT ones in the resulf of mixed models? [closed]

I read, that there are many methods of determining the degrees of freedom, thus calculating the p-values for fixed effects in mixed models. I read, that the worst is the Wald test and the Log-...
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Singularity issue, caused by polynomial regression, in the wald test of significance

I am trying to explain the housing sales prices and need for it to include the squared terms of some variables, for instance distance to the nearest forest, in order to capture the real effect. This ...
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Comparing LM, LR and Wald Test in Logistic regression model

I want to test omitted variables and I perform 3 tests: $Wald$, Likelihood Ratio ($LR$) and Lagrange Multiplier ($LM$) test. My model is a linear model with a polynomial element ($x^2$). I found a ...
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