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Questions tagged [invariance]

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On the definition of maximal invariant

On page 184 of Statistical Models by A. C. Davison, he states that It (an invariant $a(Y)$) is maximal invariant if every other invariant statistic is a function of it, or equivalently, $$a(y) = ...
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Spherical distribution counterexample

Let $X \in \mathbb{R}^{n \times p}$ be a random matrix. The distribution of $X$, call it $F(X)$, is said to left-spherical if for any orthogonal matrix $O$ such that $O'O = I_n$, $F(OX) = F(X)$. ...
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Multi-group SEM: what steps in measurement invariance

Sorry for asking a stupid question but I had been struggling for quite a while now. I'm not sure what steps to talke to evaluate a moderating effect in a path analysis model. I now have a path ...
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Evaluating measurement invariance with lavaan and ordered data

I am running a measurement invariance in lavaan in R. I am comparing a measure of sociocultural appearance pressures across White and Black women. Because this is a 5-point scale, I am treating the ...
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Can Mplus run invariance testing if you only have access to summary data

Does anyone know if you can run invariance testing if you only have access to summary data. I have one data-set with full item level information and can only access summary data on another data-set (...
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AMOS: CFA testing invariance, but cannot name intercepts

I'm using AMOS to run a 2-factor model with 5 indicators each (10 in total). I'm assessing the invariance. So I'm assessing the invariance for sex. While the configural and metric invariance worked ...
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Why is invariance (in relation to neural networks) called invariance?

Why is the property of neural networks being robust to variances in the input referred to as invariance? Is it that the neural network's output is invariant, regardless of a variance in the input?
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What is Exact definition of Invariance principle

Books wrote a lot about invariance definition and method to obtain invariance estimators, tests, and etc. However I couldn't find exactly the definition of principle of invariance. Is there any good ...
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How to show a hypothesis test is invariant under some transfomation?

How Can I show a test statistics invariant under specific transformation like shift or scalar or orthogonal transformation. Is there any routine way to do that? Is it enough to show that test ...
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Is the invariance property of the ML estimator nonsensical from a Bayesian perspective?

Casella and Berger state the invariance property of the ML estimator as follows: However, it seems to me that they define the "likelihood" of $\eta$ in a completely ad hoc and nonsensical way: ...
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multi stage sampling without independence

I have a question regarding multi-stage sampling. To keep it simple, let's consider two stage sampling. Let p1 be the probability of picking a cluster at stage 1 using the Bernoulli sampling process. ...
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Find the invariant measure $\pi=(\pi_{1},\pi_{2},\pi_{3})$ for a Markov Chain with transition matrix given

Let $(X_{n})_{n\in\mathbb{N}_{0}}$ be a Markov Chain with state space $M=\left\{x_{1},x_{2},x_{3}\right\}$ and transtition matrix $$ \Pi=\left(\begin{array}{ccc}p_{1} & p_{2} & 1-p_{1}-p_{2}\\ ...
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Is there any difference between estimating $\sigma^2$ and $\sigma$ in a simulation study?

In a simulation study, is there any difference between $\bullet$ estimating the variance $\sigma^2$, $1000$ times and taking its average, and $\bullet$ estimating the standard deviation $\sigma$, $...
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Maximum likelihood estimate of square root of mean of geometric population

We have $n$ independently geometrically distributed values: $X_{1}, X_{2}, ... $ IID ~ Geom(p) We also assume that $n$ data values $x_{1}, x_{2},...$ are available. Now I would like to find the MLE ...
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partial scalar measurement invariance

I have performed a measurement invariance analysis in R using SemTools, to assess the five factor structure of a questionnaire across 3 age groups. The latent variables have 5 indicators (5 items). I ...
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Invariance of mutual information (two-dimensional Gaussian)

I encountered a putative contradiction. Assume we have two 2-dim. Gaussian variables $z_1 = (x_1, y_1)$ and $z_2 = (x_2, y_2)$ with all components being independent, normal distributed variables: $x_1,...
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Ways of implementing Translation invariance

Is there any literature about the different ways translation invariance can be achieved when classifying images with Convolutional Neural Networks? Aside from using the structure of CNN, did anyone ...
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Getting different r-square values whe constraining the models to be equal (Testing invariance in structural model)

I compared the chi-square value from the model with all parameters allowed to be unequal across groups (e.g., parameters are set free) to the chi-square from the model where paths at time-point 1 and ...
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Model panel data with ONLY time-invariant variables

I have a large dataset containing computers and their specifications. I collected 20 different prices over a period of 20 weeks for each computer. Now I want to build a model with the price as a ...
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Is Shift and Scalar invariant same as independent under linear transforms?

I saw "shift and scale invariant" terms for the first time, and I'm wondering what's their meaning? in other word: Is Shift and Scalar invariant same as invariant under linear transforms? thanks.
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Conceptual help with scalar invariance testing

I'm having trouble understanding why scalar invariance is needed in testing a certain type of model. Let's say I have employee and supervisor ratings of deviance. I want to look at what happens when ...
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Metric invariance: CFI difference test and Chi square difference test. What happens when contradictory results are found?

I have been examining a sample (n > 600) for metric invariance, using AMOS. Using the Comparative Fit Index (CFI) difference test, which seems to be free of sample size influence, I get evidence of ...
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Measurement Invariance

My colleagues and I are analyzing data by using multi-group SEM. Background We would like to know how individuals' commitment in a specific leisure activity influences their well-being. Specifically,...
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Example for a prior, that unlike Jeffreys, leads to a posterior that is not invariant

I am reposting an "answer" to a question that I had given some two weeks ago here: Why is the Jeffreys prior useful? It really was a question (and I did not have the right to post comments at the time,...