Questions tagged [scale-invariance]
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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 ...
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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 ...
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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/...
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Measurement Invariance For Sigle-Item Binary Measures (Between Participants)
I have a dataset in which 900 people responded to a single-item binary outcome variable. However, each of the individuals responded to only one of three different binary measurements.
This would ...
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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 ...
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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 ...
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Scale dependent solutions for scale-invariant cost function in nonlinear regression
Suppose, I have a nonlinear regression problem, where I have the lables of my training data $\bf{y}$ and two measurement matrixes $A$ and $B$. The cost function is $\Vert \frac{A*\textbf{w}}{B*\textbf{...
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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 ...
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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 ...
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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(\...
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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).
...
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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 ...
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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.
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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 ...
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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 ...
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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 ...
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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 ...
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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) ...
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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 ...
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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[\...
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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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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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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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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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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 ...
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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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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):
...
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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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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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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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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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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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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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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 ...
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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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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,
$$
under sufficient regularity conditions in terms of moments. For ...
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Intensity of fractional Gaussian noise
I try to understand the 2nd formula stated in the picture. It yields the intensity/volatility of an fGN process. It depends solely on H ?? Why is that?
How is this volatility different from simply ...
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Is Shift and Scalar invariant same as independent under linear transforms?
I saw "shift and scale invariant" terms for the first time, and I'm wondering what's their meaning? in other word: Is Shift and Scalar invariant same as invariant under linear transforms?
thanks.
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Conceptual help with scalar invariance testing
I'm having trouble understanding why scalar invariance is needed in testing a certain type of model.
Let's say I have employee and supervisor ratings of deviance. I want to look at what happens when ...
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Parametrisation invariance/covariance of the Jeffreys prior
I've been trying to understand what exactly is meant by parametrisation invariance of the Jeffreys prior.
Already I've read here that invariance is technically not the best term to use, and that it'...
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RMSE is scale-dependent; is RMSE%?
I've got a graph of RMSE% vs. unit size and it declines nicely. Is this scale-dependence or does the "%" compensate for that?
$$ \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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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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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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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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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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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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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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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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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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