Skip to main content

Questions tagged [scale-invariance]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
3 votes
1 answer
43 views

Suppose $(X,Y)$ have copula $C(u,v)$, does $(aX,aY)$ have the same copula for $a>0$?

Suppose $(X,Y)$ have copula $c(u,v)$ in the sense of $Pr(X\leq x,Y\leq y)=Pr(F_X(X)\leq F_X(x),F_Y(Y)\leq F_Y(y))=Pr(U\leq u, V\leq v)=c(u,v)$, where $u\equiv F_X(x)$ and $v\equiv F_Y(y)$ and $c(u,v)$ ...
ExcitedSnail's user avatar
  • 2,966
4 votes
1 answer
82 views

Why do I get smaller degrees of freedom for the Scalar invariance model than the Metric one while testing measurement invariance?

I am trying to test the measurement invariance in my bi-factor model with CFA tests. I have 23 binary questions coded "correct" and "incorrect" and 3 different groups in my data. ...
Enes Bayrakoglu's user avatar
0 votes
1 answer
108 views

Measurement invariance: Model fit increases with increasing constraints

I have run into the same problem repeatedly, namely that model fit increases with increasing model restraints. I want to compare measurement invariance on a three-factor model (based on previous CFAs ...
Viktoria Birkenæs's user avatar
0 votes
0 answers
18 views

Can I move on to the next level (test) of invariance when my fit gets better?

I am running a group invariance test. The data consists of data from students from grades 5 and 6 for one school (School A) and only from grade 5 in another school (School B). I have already run group ...
EmH's user avatar
  • 315
1 vote
0 answers
23 views

Failure to meet the Scalar Invariance model

I did an 6 group experiment and I ran the multi-group CFA and failed to meet the Scalar model. I understand that the analysis should not compare means in that case but I can do MANOVA and SEM/...
Jennifer Lau's user avatar
2 votes
0 answers
85 views

Is AIC scale invariant for problems concerning the number of data points in regression?

I am trying to use Akaike Information Criterion with the small sample correction (AICc) as method for determining how many data points to use in a linear approximation of a non-linear function; the ...
Glen Mackey's user avatar
1 vote
1 answer
95 views

Do you lose information when you encode numerical columns with two values?

Sometimes I have numerical columns that are composed of two unique values. For example, a value from the set $\{0.1, 5.4\}$ in every cell, or $\{-1, 0\}$ in every cell. I typically scale these columns ...
Connor's user avatar
  • 655
1 vote
1 answer
374 views

Comparing multigroup CFAs: Improved fit with more restrictions

I have conducted a CFA for a one-factor measurement model and then proceeded to do multigroup CFAs to test for measurement variance for gender and age (binary variable, median split). Testing for ...
André's user avatar
  • 103
0 votes
0 answers
21 views

Ask for rationale of finding the corresponding prior from regularizer by taking exponential of negative regularizer

In equation (5.112) of textbook "Pattern Recognition and Machine Learning" by Christopher M. Bishop, the simple regularizer takes the form $\frac{\lambda}{2}{\bf w}^T{\bf w}$. The author ...
zzzhhh's user avatar
  • 333
1 vote
0 answers
29 views

Where is the h function of the exponential family gone?

The problem comes from equation (4.86) of text "Pattern Recognition and Machine Learning" written by Christopher M. Bishop $$a_k({\bf x})={\bf\lambda}_k^T{\bf x}+\ln g({\bf\lambda}_k)+\ln p(\...
zzzhhh's user avatar
  • 333
0 votes
1 answer
351 views

Which is the measurement invariance level necessary for a multiple regression analysis?

I am interested in running a multiple regression model to test the association between a predictor variable x and an outcome variable y and control by some confounders variables (e. g. gender, age). ...
Mirtes Garcia Pereira's user avatar
1 vote
0 answers
86 views

Scale-free network or not?

I am working on a directed graph, where in and out degree distributions are extrimely different: while the in-degree is for sure following a power-law, the out degree is not. Also, the in degree is a ...
Placido Pellegriti's user avatar
2 votes
0 answers
334 views

CNNs Scale/Rotation Invariance

CNNs are translation-invariant due to the pooling layer. How can we make them scale/rotation invariant? I have beginner-level knowledge of Deep Learning so please help me understand.
Murtaza Kazmi's user avatar
0 votes
0 answers
25 views

Effect of scaling data on ARMA coefficients [duplicate]

For numerical stability, I thought it might be a good idea to scale my data before feeding them into an ARMA GARCH model. I have gone through a few older posts and understand the affect scaling ...
CBBAM's user avatar
  • 311
0 votes
1 answer
213 views

Effect on GARCH innovations after scaling by a constant

I wish to fit the innovations resulting from a GARCH (1,1) process to either a student-t or an NIG distribution. For stability, I had to scale my data before applying GARCH. How will this affect the ...
CBBAM's user avatar
  • 311
2 votes
1 answer
715 views

Should I scale my dataset before applyting VAR?

I need to implement a VAR (vector autoregressive) model using a dataset of multiple financial indices. The dataset is unscaled. Should I scale it first or the VAR is not sensitive to scaling? In case ...
Luigi87's user avatar
  • 213
6 votes
3 answers
3k views

What does it mean to say that a regression method is (not) "scale invariant"?

I was just studying partial least squares regression, and I read that it is "not scale invariant". What does "scale invariant" mean, and why is partial least squares, and why would ...
The Pointer's user avatar
  • 2,086
2 votes
0 answers
26 views

Does rounding violate the restrictions of an interval scale?

I'm currently working with questionnaire data from the NASA TLX. It uses a graphical rating scale with 100 equally spaced data points, broken up by 21 ticks, leaving intervals of 5. Its manual (p. 4) ...
Dom42's user avatar
  • 115
1 vote
0 answers
18 views

Description of how the count of binary patches and their size is affected by noise?

In acoustics, signals can be represented as a matrix $M$ in time, frequency, and amplitude. Obviously the signal we want to describe is always superposed over other noise, $N$: One way to analyze ...
Halyn Betchkal's user avatar
0 votes
1 answer
460 views

Show that Y is a pivotal quantity [closed]

Let $X_1, X_2,..., X_n$ denote a random sample from $Unif(0,\theta)$. Find a function of the MLE for $\theta$ that is a pivotal quantity. I have the sampling distribution of $X_n$, $f_{x_n}(x)=n[\...
kbreak22's user avatar
4 votes
1 answer
280 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 ...
Mon2's user avatar
  • 43
0 votes
1 answer
533 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 ...
JamesCraemer's user avatar
4 votes
1 answer
624 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 ...
socialscientist's user avatar
2 votes
1 answer
2k 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 ...
JJchry's user avatar
  • 23
6 votes
2 answers
1k views

Do parameters stay unchanged when GARCH is scaled?

Let's say we have a GARCH($1,1$) process specified as follows: $y_t = \epsilon_t \sqrt h_t, \quad \epsilon_t \sim N(0,1) \quad \text{i.i.d.}$ $h_t = a_0 + a_1 y^2_{t-1} + b_1 h_{t-1}.$ If we were ...
Vykta Wakandigara's user avatar
-1 votes
1 answer
53 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 ...
David's user avatar
  • 1,276
0 votes
1 answer
630 views

log-likelihood value (switching from positive to negative)

I have a question about M.L estimation. When I estimated the AR(1)- GARCH(1,1) using log returns, the value of the log-likelihood is positive (see bellow): ...
Feijao's user avatar
  • 1
1 vote
2 answers
167 views

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?
screeb's user avatar
  • 225
7 votes
1 answer
536 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 ...
user56834's user avatar
  • 2,877
10 votes
3 answers
12k 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 ...
Upendra01's user avatar
  • 1,956
5 votes
2 answers
3k 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 ...
can_glospul's user avatar
1 vote
1 answer
222 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 ...
John Smith's user avatar
1 vote
1 answer
2k 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 = ...
Meagan's user avatar
  • 21
0 votes
1 answer
70 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): Imagine ...
Flo's user avatar
  • 159
4 votes
2 answers
1k 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-...
Leonid's user avatar
  • 255
1 vote
0 answers
128 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 ...
Alexander Sokol's user avatar
1 vote
0 answers
46 views

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 ...
user3817704's user avatar
2 votes
2 answers
420 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.
SirSaleh's user avatar
  • 339
2 votes
0 answers
172 views

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 ...
user102939's user avatar
7 votes
1 answer
454 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'...
Timsey's user avatar
  • 551
6 votes
1 answer
8k 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 ...
J Kelly's user avatar
  • 517
1 vote
0 answers
69 views

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 ...
nisr's user avatar
  • 85
7 votes
3 answers
2k 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? ...
user7064's user avatar
  • 2,207
4 votes
2 answers
697 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 ...
pixels's user avatar
  • 649
7 votes
2 answers
3k 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.
johnny's user avatar
  • 135
3 votes
1 answer
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 ...
Opt's user avatar
  • 747
2 votes
1 answer
40 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 ...
bayerj's user avatar
  • 13.8k
2 votes
0 answers
256 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 ...
Ehsan88's user avatar
  • 283
5 votes
1 answer
2k 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....
Jeremyjaytaylor's user avatar
2 votes
1 answer
3k 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 ...
Jeremyjaytaylor's user avatar