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Questions tagged [wald-test]

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

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Likelihood-ratio and score tests of a (non)linear combination of coefficients

The likelihood-ratio and score test are typically used for simple scalar hypotheses such as $\beta_1 = 0$ or $\beta_1 = \beta_2 = 0$. How can we test a linear combination of coefficients using the ...
DrJerryTAO's user avatar
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2 votes
1 answer
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Hypothesis tests in summary of glm() are always Wald tests?

The summary output of glm() in R uses t-statistic when dispersion is estimated and z-statistic when dispersion is not estimated. I want to know if both tests are ...
quibble's user avatar
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Prove Wald statistic = number of linear restrictions times F statistics

I'm considering $F[J,n-k]= \displaystyle \frac{(e_{*}^{'}e_{*}-e'e) \backslash J}{e'e\backslash (n-k)}$, where $J$ stands for number of restrictions. I want to prove $W=(Rb-q)'(Rs^2(X'X)^{-1}R')^{-1}(...
Chang Henry's user avatar
7 votes
2 answers
105 views

LR statistics add up for nested models. What about the Wald test?

Consider models M0, M1, M2. Let M0 $\subset$ M1 $\subset$ M2, i.e. let the models nest each other. I test the following pairs of models using the likelihood-ratio (LR) test: M0 vs. M2, M0 vs. M1, M1 ...
Richard Hardy's user avatar
2 votes
1 answer
61 views

How does the Wald test follow a chi-square distribution? (Do we ignore independence)

So, according to the definition, a statistic follows a chi-square distribution if we square and add independent and standard normal variables right? So for the Wald test (Chi-square version), we are ...
chunguc1004's user avatar
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How to get an overall P-value for a categorical variable, If I know the t-values of its dummy variables?

I am doing ANCOVA: main categorical variable for the comparison is "Street" and it contains 3 categories (Street1, Street2 and Street3). The outcome variable is social interaction time (...
Hussain's user avatar
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1 answer
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How to interpret DESeq results with LRT vs. with Wald's test

I am new to the field of RNA-Seq and wanted to ask for advice concerning the proper use of the two DESeq() test options (LRT vs. Wald test). Briefly, my ...
Luise Charlotte's user avatar
1 vote
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58 views

In what scenarios can we use Wald confidence intervals

In my stats course we derived Wald confidence intervals using properties such as asymptotic normality of the maximum likelihood estimator. This asymptotic normality relies on a statistical model being ...
delta_99's user avatar
4 votes
1 answer
87 views

Does the "log-likelihood" measure cover all details about model fit, like covariance structure, adjustments, robust variance estimator, etc?

Just a general statistical question: when any statistical software returns log-likelihood of some model, does it account for all details in it? For example, when we employ generalized least square ...
NadirCamzani's user avatar
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Can be any example of testing contrasts using Wald's approach reproduced with Likelihood Ratio testing?

For illustration I will use R, but the question is general statistical question, totally not R related. Assume I have a numerical variable and categorical variable with 3 levels, like A, B and C, for ...
NadirCamzani's user avatar
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calculate effect size from regression table

I am working on power analysis for a project. I want to benchmark effect size from another study. How can I find the effect size (Cohen's d) just by looking at the regression table below? For instance,...
YouLocalRUser's user avatar
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Hypothesis test for treatment with opposite signed effects across subgroups

Imagine a treatment that, if it has an effect, is likely to affect two groups in opposite directions. As a concrete example, suppose I am testing the effect of a Republican politician endorsing a ...
ChrisP's user avatar
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1 answer
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Comparing cross-lagged coefficients in Mplus (Wald chi-sq test)

I'm running a cross-lagged panel model analysis in Mplus. The cross-lagged path coefficients were constrained to be equal across time. Now, I'd like to test if the cross-lagged path from MSC to MA and ...
hakim's user avatar
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How to compare 2 estimates from a model fitted by MLE when the covariance of the estimate can't be always estimated?

I have one model, that I fit using MLE. In order to feel what could be a good initial guess for the fitting process, I try different arbitrary smartly chosen initial guess (not random) and report the ...
Jerem Lachkar's user avatar
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20 views

Statistical difference per group

I am calculating elasticities per income quintiles. I have 10,000 observations of elasticities calculated for each quintile, so a dataset of 5*10,000. I would like to test whether the elasticities are ...
Stata_user's user avatar
5 votes
1 answer
166 views

svychisq with statistic="Chisq" vs. statistic="adjWald"

I'd like to run analyses using Rao-Scott Chi-squared test using svychisq to account for survey weights. It seems that statistic="Chisq" gives the Rao-Scott version, however, now that I'm ...
AskingSomeQuestions's user avatar
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1 answer
840 views

What is the difference between z-value and the Wald statistic in the summary function of the Cox Proportional Hazards model of the “survival” package?

When I run the code posted at the bottom (using the summary() function of the R survival package, I get the output shown ...
Village.Idyot's user avatar
1 vote
0 answers
64 views

Wald Test Statistic for an M-estimator

Suppose we are interested in the following hypothesis: $$H_0: h(\theta)=0\quad versus\quad h(\theta)\neq 0,$$ and we have an usual M-estimator for $\theta$ such that $$\sqrt{N}(\widehat{\theta} -\...
MinChul Park's user avatar
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328 views

From Wald test statistic to P-value

Lets say I have a dataset with a binary target variablem, smoker / non smoker, and a continuous variable of miles running per week. So for each catigory (smoker or <...
Programming Noob's user avatar
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Fiding the test statistic, using wald test

Given the random sample $X_1,...,X_n \sim N(\mu, \sigma^2)$, I want to perform a Wald test for: $\mathrm{H}_\mathrm{0}: \mu = \mathrm{\mu}_\mathrm{0}$ $\mathrm{H}_\mathrm{1}: \mu \neq \mathrm{\mu}_\...
CORy's user avatar
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1 answer
323 views

Wald test failing to reject null hypothesis that a predictor is insignificant in regression when t-test on terms involving predictor show significance

I am running a logistic regression using a set of several predictors as well as several interaction terms. For each predictor, I am running a Wald test in statsmodels to test whether or not a ...
delsaber8's user avatar
1 vote
0 answers
442 views

the Wald, Likelihood Ratio (LR) the Lagrange Multiplier (LM) test statistics Are monotonic function of F statistics

Consider a classic linear regression model. I want to show that the Wald, Likelihood Ratio (LR) the Lagrange Multiplier (LM) test statistics for the null hypothesis $H_0: R\beta =r$ for a constant ...
1190's user avatar
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1 answer
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What does it means if two variable with exactly the same Wald Chi-Square?

After I run the program, it shows two variables with exactly the same Wald Chi-Square, how can I interpret these statistics? Can I say that it is Quasi-complete separation that a single level of a ...
Woddyopened's user avatar
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207 views

Deviance statistic vs Wald test

I have a question. I have run a logistic regression model with 5(X1,..., X5) continuous predictors. The predictor with the highest coefficient is X2, but the predictor that reduces the most deviance ...
lola's user avatar
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1 answer
28 views

How do I test whether coefficients in different models are statistically different when grouping off DV

I'm trying to see whether good players in chess (those with more than a 1250 Elo) are helped more by puzzles than bad players (those with less than a 750 Elo). Usually, the way I would do this is with ...
Eric Tim's user avatar
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0 answers
185 views

Do wald and score-tests work when we have nuisance parameters?

Do wald and score-tests work when we have nuisance parameters? In statistics, a nuisance parameter is any parameter which is unspecified ${ }^{[1]}$ but which must be accounted for in the hypothesis ...
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2 votes
1 answer
114 views

Does the one-tailed vs two-tailed argument apply in GLMs (i.e. Wald test) in the same way it would in a Student’s t-test?

I have constructed a gamma glm modelling hormone concentration with three predictors: treatment (treatment or control), sex (male or female) and site (thyroid, parathyroid). The work is mostly ...
willpkay's user avatar
2 votes
0 answers
62 views

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$(1, p_1$), $Y_1, ..., Y_{n_2}$ ...
Chris's user avatar
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2 votes
0 answers
31 views

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 ...
Mark Calhoun's user avatar
2 votes
1 answer
871 views

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 ...
fmtcs's user avatar
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3 votes
0 answers
91 views

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 ...
Tereira's user avatar
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-1 votes
1 answer
530 views

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 ...
Hermi's user avatar
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1 vote
0 answers
433 views

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\}$...
Working dollar's user avatar
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0 answers
163 views

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 ...
daemon's user avatar
  • 21
0 votes
1 answer
34 views

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 ...
Arzental's user avatar
0 votes
1 answer
1k views

Wald test for sum of coefficients in R

I am "translating" code from STATA to R, and need to translate the following command: ...
Nate 's user avatar
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4 votes
1 answer
784 views

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 ...
Michael Gmeiner's user avatar
2 votes
1 answer
329 views

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 ...
myfatson's user avatar
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2 votes
1 answer
48 views

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}=...
Hermi's user avatar
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2 votes
0 answers
46 views

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 ...
Federico Tedeschi's user avatar
0 votes
0 answers
814 views

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 ...
BoudSTER's user avatar
2 votes
1 answer
1k views

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 ...
Greenhill's user avatar
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0 votes
0 answers
104 views

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):...
Zeinab Elashidy's user avatar
0 votes
1 answer
193 views

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-...
Krapatik321's user avatar
2 votes
1 answer
1k views

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. ...
silverferry's user avatar
2 votes
0 answers
291 views

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 ...
Matthew Coudert's user avatar
0 votes
1 answer
854 views

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 ...
Michiel's user avatar
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1 vote
0 answers
185 views

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 ...
christoffer ku's user avatar
15 votes
3 answers
4k views

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, ...
Single Malt's user avatar
2 votes
0 answers
33 views

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 ...
user45523's user avatar
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