# Questions tagged [robust]

Robustness in general refers to a statistic's insensitivity to deviations from its underlying assumptions (Huber and Ronchetti, 2009).

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### Robust Maximum Likelihood Estimator on AMOS? [closed]

Does anyone have suggestions or has been able to utilize the robust maximum likelihood estimator on AMOS? Thank you!
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### The function step.lmRob() is not working [closed]

I have a linear model, which i analyzed (in R) through: lmrob_object<-lmrob(diff_mg ~ age + bmi + energy + fiber + ca + phos + iron + potas + supp + uni, data = data), where: diff_mg is the DV (...
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### Intercept significant, but confidence intervals around its standardized β include 0

I ran a HC (‘robust’) regression. The intercept is significant, which is reflected in the confidence intervals around the unstandardized betas. However, the CIs around the standardized β are quite ...
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1 vote
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### What is the interpretation of outlier-robust principal component analysis?

There's a set of methods called "robust" principal component analysis (here, "robust" means resistant to influence from outliers). One example is Hubert et al., "ROBPCA: A new ...
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### Improving Robustness of LSTM Model for Stock Price Prediction

I am currently working on a Long Short-Term Memory (LSTM) model for predicting stock prices. My model takes into account the fact that there are non-trading minutes with no data. I have also ...
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### Why does R robustbase and rrcov covMcd compute reweighted step trimming adjustment with actual fraction of outliers?

covMcd and CovMcd in R robustbase and rrcov compute by default a reweighting step. Reweighting in MCD and similar computes the Mahalanobis distances and the uses a cutoff using the chisquare ...
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### Binary response vs probability response

Consider these two scenarios: respondents are asked to choose between two options offered to them (the resulting data is binary 0 & 1) respondents are asked to give their probability of choice ...
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1 vote
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### Robust estimation of standard deviation using relatively small sample taken from a Gaussian distribution

I'm sure this question was asked before, but I don't seem to be able to find a convincing answer. If there is a relatively small set (say 3<n<20) of observations of a quantity that is assumed to ...
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### ANOVA vs Kruskal Wallis - Small sample size

I have data from an experiment comparing plant weights for 4 independent treatment groups. The data seem to be normally distributed (I have been warned about using statistical tests for normality). ...
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### Determine a robust trend from noisy time series data, when start and end years have a material effect

I have about 20 years of data, each year has a number of observations. If I put a linear trend through the data, I get a trend, and this trend differs based on the the choice of start and end year, ...
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### Repeated measure (2 situations) with skewed data and a covariate

I made repeated measure of all participants in 2 situations (situation A and B) for devaluing comments (devComnts) as outcome (measured as proportion: devaluing comments / all comments). Distributions ...
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### Standard deviation of an autocorrelated time series

Given a time series of log returns $R_t$ with significant autocorrelation up to $k$ lags, what is the formula for the standard deviation of $R_t$ that accounts for this autocorrelation? I've seen the ...
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### Position M-estimators are affine equivariant (proof)

A position M-estimator of $\mu$ is defined as the solution of the equation (it is a $\mu$ such that): $$\sum^{n}_{i=1} \psi\left(\frac{x_i - \mu}{ \sigma_0 } \right) = 0$$ ($\psi(x)$ is even and non-...
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### Dummy regression group comparison

I want to do my ANCOVA as a robust regression as assumptions are hurt. I have a categorial predictor with 5 groups but I also want to check pairwaise for all groups if they differ in their effect on ...
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### Polynomial fitting from robust linear mixed effects model

I have run a robust linear mixed effects model to determine the standard deviation within subjects for a repeatability study on a new imaging device. The SDw was derived from the square root of the ...
1 vote
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### How to do an interaction in lmRob() function?

I am trying to compare 2 lmRob() models. One for male and one for female gender. Imagine my model like this: ...
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### How to compare multiple linear regression statistically? [duplicate]

I am looking for a way to compare the results from two lmRob() functions statistically. Here is an explanation what I am trying to do: My professor wants me to compare the results of two ancovas (one ...
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1 vote
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### How can I compare the results of two lmRob() models? [closed]

I am looking for a way to compare the results from two lmRob() functions statistically. Would that be a possible option for me: lmrob_female <- robust::lmRob(Y ~ X_binary + covariate1 + covariate2 +...
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### Robust Difference-in-Differences: What is the propensity score doing?

Callaway and Sant'Anna (2022) describe a doubly robust difference-in-differences (DiD) method that is attractive in staggered DiD (multi-group treatment times) for several reasons. It can prevent &...
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### Robust ANOVA t2way unequal sample sizes?

I have some parameters that I would like to analyze with a two-way ANOVA. The treatment groups have unequal sample sizes (n=9, n=36, n=36, n=36) and the data do not fulfill the requirement of normal ...
1 vote
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### Perturbation for more stable convex optimization

I am thinking of adding some perturbation to my convex optimization problem. The idea is straight forward like below chart. Supposed you are solving $\text{argmax} f(x)$, we want to find an $x$ that'...
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### Sequential prediction/modeling without stationarity assumptions

Let's say that we have an arbitrary real-valued sequence of length $n$: $$(x_{i})_{i \in \{0, \dots, n-1\}}.$$ If we wanted to try to create a probabilistic model for future values of the sequence ...
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### How does Huber compute the $\operatorname{var}(s_n)/E[s_n]^2$ and $\operatorname{var}(d_n)/E[d_n]^2$?

(N.B. I am cross posting this question from math stackexchange since after x days I have still not received any responses.) How does Huber in book 'Robust statistical procedures' in chapter 1 compute ...
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### Interpet coefficient estimates with log(Y) in rdrobust package

1.I want to interpet the coefficients of RDD model above. The dependent variable is log-transformed. Should it be the same as linear regression even though I am using local polynomial regression with ...
1 vote
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### How to implement an S-estimator

I'm trying to implement an MM-estimator in python. I have a working implementation of an M-estimator statsmodels.RLM - which is implemented as an iteratively re-weighted least squares algorithm. I am ...
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### Effect of robust maximum likelihood estimator in structural equation modelling when data is normal?

I understand that when data are nonnormal robust maximum likelihood estimator can be used. I'm wondering are there any disadvantages of using a robust maximum likelihood estimator when the data are ...
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### Structural equation modeling (latent growth models): robust estimators to handle outliers?

Can I use robust estimators (e.g., "MLM" and "MLR"estimator lavaan options) to overcome outliers within my sample, or should I remove outliers? For context, I am modelling the ...
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### How are robust standard errors applied in logistic regression

I have been reading up on robust standard errors and had a few questions regarding how their use in logistic regression. I have read here that heteroscedasticity is not an issue in logistic regression ...
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### Robustness check in Structural Equation Modelling (SEM) in R

I have conducted SEM analysis in R and used Maximum Likelihood Robust estimator as my data are categorical and deviate from multivariate normality. when I submitted my manuscript, one reviewer asked ...
1 vote
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### Influence function of the IQR

In class I am told the influence function of the IQR should be a constant times the difference between the influence function for the 75th percentile and the influence function for the 25th percentile,...
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### How do you use ordinal response data with several random effects to do robust hypothesis testing?

I want to explore the roles of lung presence and habitat on tadpoles' ability to tolerate low oxygen levels. My experimental design generated several measurements of "responsiveness" (on an ...
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### Outlier detection for observations with sinusoidal relationship, incomplete information

I was looking for recommendations for an outlier rejection problem I find myself needing to solve. I have a set of measurements (12 at a time) which vary sinusoidally according to  d = \begin{...
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### Model comparsion for robust linear mixed models (robustlmm)

I'm currently working on a project where I've fitted 4 robust linear mixed models. However, I've hit a bit of a roadblock when it comes to model selection. I've been using the AIC (Akaike Information ...
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### Anova violates normality assumption for error data

I have a 2 x 2 repeated measures ANOVA (N = 51) with Error Rate data as the dependent measure. The error data violates the normality assumption, even when outliers are removed. I have looked at the ...
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### Robustness of Mann Whitney U Test for partially paired data

I'm curious if anyone is aware of a publication that addresses the following matter or could provide a mathematically or reasonable response to the following question: In a pre-post study where ...
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### Reconciling Nondeterministic and Probabilistic Decision Rules

I've been getting a bit stuck recently on how to reconcile the two seemingly-competing ideas of nondeterministic and probabilistic decision rules. As an example: Let $t=0$ denote the current time and ...
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### Mediation model with non-normal data

I want to conduct a mediational analyses with three variables: Predictor: it is the result of a memory test with range -1 to 1. Mediator: it is the absolute error made by the participant when ...
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### Is this algorithm for robust estimation of the covariance matrix sensible?

I have a high dimensional dataset $\bf{X} \subset \mathbb{R}^d$, which is multimodal and has outliers. I want to estimate a robust measure of association, something like the correlation between two ...
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### Modeling outliers in maximum likelihood estimation with gradient descent

Consider a set of 3D points $X = \{x_1, x_2, ...x_n\}$ with $x_i\in\mathbb{R}^3$ on which we want to fit an arbitrary probability distribution. The distribution we want to fit models some ...
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### pros and cons of different robust measures of scale/ dispersion

I would very much appreciate some help regarding how to interpret different robust measures of scale (Inter-quartile range or IQR, biweight midvariance, and median absolute deviation or MAD). Thus, ...
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### How to determine if my model is robust? Should the coefficients be same?

I want to run robustness tests for my model. For example, by reducing the sample to heavily concentrated groups, running a different regression (probit etc) etc. But, how do I ascertain that my ...
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1 vote
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### Proving upper bound for Bias of truncated sample mean

We have data $X_1, \dots, X_n$ which are i.i.d copies of $X$. Where we denote $\mathbb{E}[X] = \mu$, and $X$ has finite variance. We define the truncated sample mean: \$\begin{align} \hat{\mu}^{\...
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### Robust ANOVA using the WRS2 Package: One way repeated measures of ANOVA [closed]

I'm unable to use the rmanova function in the WRS 2 package that computes a one-way repeated measures ANOVA (see page 25). ...
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### When can I ignore endogeneity problem?

Technically, endogeneity occurs when a predictor variable (x) in a regression model is correlated with the error term (e) in the model. This can occur under a variety of conditions, but two cases are ...
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