Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [optimal-scaling]

Optimal scaling or optimal quantification is an algorithmic approach to transform categorical variables into scale (interval) ones which would be "optimal" in some statistical sense (for example, their linear correlations will be maximized). There exist nonlinear "optimal scaling versions" of many classic linear kinds of analysis, including regression, PCA, etc.

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Can I use optimally scaled variables for a factor analysis to account for rotation? If I can then how?

I have discussed this issue several times in this site, but I am asking it again for a final justification from the experts of our community. I wanted to extract four factors (I should call dimensions here I think) from a CATPCA along with the…
Blain Waan
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How to calculate Rousseeuw’s and Croux’ (1993) Qn scale estimator for large samples?

Let $Q_n = C_n.\{|X_i-X_j|;i < j\}_{(k)}$ so for a very short sample like $\{1,3,6,2,7,5\}$ it can be calculated from finding the $k$th order static of pairwise differences: 7 6 5 3 2 1 1 6 5 4 2 1 2 5 4 3 1 3 4 3 2 5 2 1 6 …
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How can I use optimal scaling to scale an ordinal categorical variable?

In an answer to this question about treating categorical data as continuous, optimal scaling was mentioned. How does this method work and how is it applied?
Freya Harrison
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How can we verify the intuition that in the RW-Metropolis-Hastings algorithm with Gaussian proposal too small and too large variances are bad choices

Let $d\in\mathbb N$ and consider the Random Walk Metropolis-Hastings algorithm with a Gaussian proposal kernel $Q$ such that $Q(x,\;\cdot\;)=\mathcal N_d(x,\sigma^2_dI_d)$ for all $x\in\mathbb R^d$. Intuitively, if $\sigma$ is too small, nearly all…
0xbadf00d
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How does the celebrated result about the diffusion limit of the Random Walk Metroplis-Hastings algorithm help us to find the optimal scaling

Let $d\in\mathbb N$ with $d>1$ $\ell>0$ $\sigma_d^2:=\frac{\ell^2}{d-1}$ $f\in C^2(\mathbb R)$ be positive with $$\int f(x)\:{\rm d}x=1$$ and $g:=\ln f$ $Q_d$ be a Markov kernel on $(\mathbb R^d,\mathcal B(\mathbb R^d))$ with…
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Scaling regression coefficients Take 2: Gelman (2008) approach

I am asking a follow-up question about interpreting regression coefficients that have been scaled following Gelman's (2008, 2009) recommendations. Original recommendation to divide continuous predictor by 2…
ksroogl
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Scaling step in Baum-Welch algorithm

I am implementing the Baum-Welch Algorithm for training a Hidden Markov Process, to basically better understand the training process. I have implemented the iterative procedures described in Rabiner's classic paper. My Implementation is in Wolfram…
Vahagn Tumanyan
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What is the advantage of transforming variables from nominal to ordinal/numerical when it reduces variance explained in CatPCA?

Context I have a dataset of 8 categorical variables. And I want to apply Categorical Principal Component Analysis (CatPCA). Before doing that, I have been advised to look at the transformation plots of all these variables after transforming them…
Tune
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Estimate the asymptotic efficiency of a Markov chain sampling by the method of batching

In the paper Efficient Metropolis Jumping Rules, the author is writing that he used "the method of batching" for the estimation of $\operatorname{eff}_{\overline\theta_i}$ in Table 1 (on page 605). Could somebody explain to me what he is actually…
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Parametric Surface Reconstruction from Contours with Quick Rescaling

I'm looking to construct a 3-D surface of a part of the brain based on 2-D contours from cross-sectional slices from multiple angles. Once I get this shape, I want to "fit" it to another set of contours via rescaling. I'm aspiring to do this in the…
DavidShor
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scaling for SVM destroys my results

I'm applying standard 0-1 scaling of features before SVM classification for financial data but the results are worse. This is the results before scaling NORMAL DATA AVERAGE RESULTS Profit PF avMC avPP avRC…
Krzysztof Fajst
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Is it possible to scale the mean and std of estimated rate/period, to another period?

Hello, all. When it comes to calculating the average from some time-spanning date, let's say the average of 20 weekly sales records from a specific store - while also calculating the standard deviation of said average value - is it possible to scale…
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How to understand optimal Scaling in R: The Package homals for novices

Does anyone know of a step-by-step guide for the practical implementation of Gifi Methods for Optimal Scaling in R: The Package homals? Although I have an OK theoretical understanding (thanks chl for directing me to articles), I'm a tech novice and…
Mike
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Optimal scaling / CATREG (categorical regression) for imputed data

I have a data set with 5 different kinds of nutrient statuses and I want to see whether they are associated with categorical / ordinal grades at school. I have multiple covariates which I will included in the analyses. Due to missing values I have…
Inge
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Can I categorize the factor scores to use them as predictors of an ordinal logistic regression?

I was wondering if I can categorize the factor saved scores by taking their quartiles (or some other measures, I am not sure what should I use!) as cut points and use them as predictors in an ordinal logistic regression. The reason I am thinking of…
Blain Waan
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