Questions tagged [scale-invariance]

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Strict Invariance - improvement in chisq enough?

I have Likert-scale data on tool preferences which I used in a cross-cultural sample that I divivided in two groups to test for invariance. I was able to find weak invariance and partial strong ...
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48 views

Invariance of maximum likelihood estimates to rearrangements of parameters/constants in the model?

I know that maximum likelihood estimates are invariant to re-parametrization (https://stats.stackexchange.com/a/335368/267430). Is the MLE also invariant to rearrangements of the constants and ...
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34 views

Testing Measurement Invariance on data with small sample size

I‘m wondering what is the best way to test measurement invariance on data with small N, since CbSEM requires at least N = 200, or 5 - 10 cases for each indicator. For example I want to test a ...
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73 views

Are confidence intervals scale-invariant?

Suppose I estimate a mean and construct some sort of confidence intervals (e.g. based on normal approximation or bootstrapped) around the mean. I now wish to rescale my mean from, say, the mean number ...
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22 views

Scale invariant comparisons of two sets of vectors

I am dealing with the following problem. Let A and B represent two sets of real-valued vectors. The vectors are of the same dimension, yet the sets contain different number of vectors. I am looking ...
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1answer
307 views

scaling in time series

I would like to know if it is fine to use scaling(Time series * constant) before applying time series. Is it similar to data transformations( log , sqrt, Box-Cox) etc or is there any implication of ...
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48 views

Multi-group SEM: what steps in measurement invariance

I'm not sure what steps to take to evaluate a moderating effect in a path analysis model. I now have a path analysis model. I hypothesized that the group moderates the relationship between variable ...
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1answer
41 views

Proving sufficiency by showing ratio of statistic pdf to sample pdf is independent of unknown parameter

Let $X_1,...,X_n$ be iid random variables with densities given by $$ f_{x_i}(x|\theta)=e^{i\theta - x}\mathbb{I}_{(i\theta,\infty)}(x), $$ when $x>i\theta $ and $x=0$ otherwise. Let $T$ be the ...
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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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1answer
251 views

Is there a “central distribution” for distributions for which the CLT doesn't apply?

The central limit theorems state roughly that under a certain set of properties of a sampling process, the distribution of a statistic from that sample will converge in distribution to the normal ...
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3k views

Why feature scaling only to training set?

I was following the book "Hands-On Machine Learning with Scikit-Learn & TensorFlow" by "Aurelien Geron". The following remark was made about feature scaling : - As with all the ...
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942 views

How do CNNs handle scale invariance?

Even after googling and reading fitting articles and answers to fitting questions here on StackExchange, I don't understand how CNNs handle scale invariance. I found logical sounding answers saying ...
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127 views

CFA vs Invariance of a test different CFI

I am currently learning how to implement CFA and invariance of constructs between two groups. My data below has two groups. So my steps are as follows Confirm the overall model works Check if both ...
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1answer
918 views

unequal group sizes in a multi-group CFA

I am testing measurement invariance across several demographic categories: age (will dichotomize), race, and BMI. The problem of unequal group sizes is most evident for racial categories: n White = ...
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58 views

Rescaling continuous scale to reduce (assumed) measurement invariance

I was wondering whether I could overcome (assumed) measurement invariance by rescaling continuous items. Example Let's say I have the following two questions (simplified for illustration): ...
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2answers
634 views

Difference between scale-space transform and wavelet transform

What is actual difference between scale-space and wavelet transform? It seems that wavelets require an orthonormal basis of kernels, whereas scale-space does not. Is it the only difference? Can scale-...
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101 views

Variance estimation for Levy process

Let $(X_t)$ be a Levy process. It then holds that $$ E(X_{t+\Delta} - X_t) = \Delta \nu, \\ V(X_{t+\Delta} - X_t) = \Delta \mu, $$ under sufficient regularity conditions in terms of moments. For ...
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Intensity of fractional Gaussian noise

I try to understand the 2nd formula stated in the picture. It yields the intensity/volatility of an fGN process. It depends solely on H ?? Why is that? How is this volatility different from simply ...
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2answers
214 views

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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1answer
159 views

Parametrisation invariance/covariance of the Jeffreys prior

I've been trying to understand what exactly is meant by parametrisation invariance of the Jeffreys prior. Already I've read here that invariance is technically not the best term to use, and that it'...
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1answer
3k views

RMSE is scale-dependent; is RMSE%?

I've got a graph of RMSE% vs. unit size and it declines nicely. Is this scale-dependence or does the "%" compensate for that? $$ \text{RMSE%} = 100\% \cdot \frac{\sqrt{\frac{1}{n}\Sigma_{i=1}^n (y_i ...
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Can I merge independent samples collected by the same survey?

I have 3 independent data sets collected from the same population using an identical survey design. They are about consumer attitudes toward foreign products, so, 3 countries of origin were used but ...
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3answers
1k views

Linear regression - results depending on the scale of the inputs

Why is there a difference in p-values for the following model $$ y = a + b_1x_1 + b_2 x_2 + b_{12}x_1x_2 + \epsilon $$ depending on the scale of the x's? ...
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2answers
512 views

Equal weight between prior probabilities

While constructing a model hierarchy for Bayesian analysis, I have two parameters: $\theta_0 \sim \textrm{Uniform}(80, 90)$ $\theta_1 \sim \textrm{Normal}(0.093, 0.002)$ I take the $\ln$ of the pdf ...
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1k views

The meaning of scale and location in the Pearson correlation context

According to wikipedia, pearson correlation is scale and location invariant. Does scale refer to "variance" and location refer to "mean" ? Thanks.
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1answer
2k views

Scale invariance for images

Given that images can be of vastly different resolutions, but neural networks are usually presented as having a fixed number of inputs, what are the standard techniques used to handle the difference ...
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1answer
33 views

Scale of variables and the consequences on the solution

Let us say I have data set of distinct $x_i$. A Gaussian is fitted to it with maximum likelihood, obtaining some $\mu$ and some $\sigma^2$. I will also obtain a likelihood $\mathcal{L}$. Now, I copy ...
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145 views

Is there any “standards” for minimum variance of likert-type measured variables?

I want to develop a questionnaire. Because the target population are children, I used 3-point likert-type scale (0 1 2) for my items. Now I want to remove invariant items (i.e. the items not having ...
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1answer
1k views

Inconsistent delta.chisq.scaled using Lavaan and semTools?

I've recently been using Lavaan and semTools to test for measurement invariance in confirmatory factor analysis (CFA) models and I noticed an (apparent) inconsistency in a calculation that confused me....
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2k views

How to extract “MLR” fit measures generated by the Lavaan package of R

I am estimating some Confirmatory Factor Analysis (CFA) models using the Lavaan package and I hoping to extract the fitMeasures to export out of the model to a spreadsheet. This is easily done using ...
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97 views

Not specifying the main effect of a term that is part of a tensor product interaction

Say you've got a model $$ y = f(X_1,X_2)+\epsilon $$ and you're OK with linear (or other parametric) functional forms. Say you think that the effect of $X_1$ on $y$ depends on $X_2$. The standard ...
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189 views

Showing $\mathbb{E}[T_n] = \theta \mathbb{E}_1[T_n]$ is scale equivariant?

This is question 5 is from Staudte and Sheather (1990), Robust estimation and testing. Let $X_1,\ldots , X_n$ be i.i.d with $$ F_\theta = F(\frac{x}{\theta}),\quad x>0;\theta>0.$$ Assume that $...
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Scaling of huge data and estimating the distribution

Suppose you have some sample of huge numbers and you want to fit some continuous distribution to these numbers. You will get some distribution that is loosely speaking highly "smeared", e.g. it has a ...
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1answer
190 views

Correlate heuristic metrics with future true performance

I am faced with a problem, that I'm pretty sure is a statistical one, but me taking 1 course in probability followed by 1 course in statistics back in university did not prepare me to adequately face ...
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2k views

Choice of weight function in Moran's I

I'm doing an autocorrelation analysis for a spatially distributed collection of observations. To perform my analysis, I am using Moran's I statistic. My questions are: (1) What are the implications ...
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1k views

Scale-invariant analysis of time series

When developing a general purpose time-series software, is it a good idea to make it scale invariant? How would one do that? I took a time series of around 40 points, and then multiplied by factors ...
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356 views

Why can scale invariance cause a loss of explanatory power?

Gary King made the following statement on Twitter: scale invariance sounds cool but is usually statisticians shirking responsibility & losing power by neglecting subject matter info What ...