Centering involves subtracting the overall sample mean score from the original score; standardizing does the same followed by dividing by the overall sample standard deviation.

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Principal Component of non-centered data and PCA-Transformation

I am reading a chapter about principal component analysis (PCA). It states that for any random varible $X \in \mathbb{R}^p$ with $n$ observations, $E[X] = \mu$ and $Cov[X] = \Sigma$ the i-th PC is ...
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1answer
10 views

Clarification on Prediction with a Regression Model using Centered Variables

As I understand it, for a regression model, centering the variables around their means can be helpful since it makes the intercept term the expected value of $Y_i$ when the predictor variables are set ...
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49 views

Centering variables in R [closed]

Do centered variables have to stay in matrix form when using them in a regression equation? I have centered a few variables using the scale function with ...
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144 views

Standardized VS centered variables

I have found many useful posts about standardized independent variables and centered independent variables on stats.exchange.com, but I am still a bit confused. I am asking you an evaluation of what ...
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54 views

How do statistics packages (e.g., fitglm in MATLAB, SPSS/SAS/Stata) handle mean centering for higher order terms? [closed]

Many questions (e.g., Centering in linear regression & How to include a linear and quadratic term when also including interaction with those variables? ) have been asked about mean centering (aka ...
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3answers
119 views

Mean centering - before regression or observations that enter regression?

I am using Stata 13 to estimate a simple model with interaction terms. To give the coefficients a meaningful interpretation at zero, and to avoid multicollinearity, I am mean centering variables. I ...
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19 views

Multicollinearity Diagnostics of Mean-Centered Interaction Terms

Interaction terms in moderated regressions exhibit high multicollinearity due to the high correlations with their main effects in case of uncentered data; for Normal distributed variables this is not ...
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30 views

Is there moderator or not? Centering and unsignificant b

I am trying to check if the relationship between X and Y is a moderated by M. Here is my model: Y = b0 + b1*X + b2*M + b3*X^2 + b4*X*M + b5*X^2*M where X - independable variable, M - moderator, Y - ...
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1answer
81 views

How should I implement this interaction between a continuous and categorical predictor?

I have a continuous outcome variable. I understand that if I have a binary predictor, and a continuous predictor, and an interaction, then the model looks like this: $y_{i} = \beta_{0} + ...
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43 views

Standardization/Centering of Longitudinally-measured variable

Could someone possibly help me with the following issues that I am mentally stuck at? Thanks so much! I have 200 variables M1, M2, .... Mx. Each is measured at three time points 0, 30, 120 min. The ...
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1answer
52 views

Centering in linear regression

I am trying to fit a quadratic to my model, I have tuples (x,y). The choices are, 1) lm(y~x+I(x^2)) 2) ...
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68 views

How does one interpret a demeaned log interaction term?

I am having problems interpreting my regression equation. I want to know the effect of an increase in variable $x$ on $y$ for different values of $z$, but as it's in logs and the interaction term is ...
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1answer
63 views

Can $x'x$ be written as correlation matrix?

$x'x=$ $$ \begin{bmatrix} \sum_{i=1}^{n}(X_{1i}-\bar X_1)^2&\sum_{i=1}^{n}(X_{1i}-\bar X_1)(X_{2i}-\bar X_1)\cdots & \sum_{i=1}^{n}(X_{1i}-\bar X_1)(X_{ki}-\bar X_k) \\ ...
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2answers
156 views

How is the first column of the matrix orthogonal to all the others

$$ \mathbf{X}_{n\times(r+1)} = \begin{bmatrix} 1 & (x_{11}-\bar x_1) &\cdots & (x_{1r}-\bar x_r) \\ 1 &(x_{21}-\bar x_1) &\cdots & (x_{2r}-\bar x_r) \\ ...
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43 views

Group mean centering predictors for crossed random effects

I'm fitting a mixed-effects model, in which I wish to test the effect of $X$ on $Y$, with crossed random intercepts and slopes for each subjects $S%$, and for each level of an additional grouping ...
4
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1answer
75 views

Zero-centering the testing set after PCA on the training set

I have a training set of data on which I do principal components analysis (PCA) and save the loadings/eigenvectors/coefficient matrix. I want to use the eigenvectors to transform my testing data into ...
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32 views

Does centering or mean normalizaiton alone every help in feature scaling?

In feature scaling, one way is to subtract the mean (centering) and then divide by the standard deviation for all data points. Suppose we just centered the data and didn't divide by the standard ...
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1answer
31 views

Should I center time variant predictors in repeated measures multilevel models?

I have a multilevel model built coinsidering repeated measures on students. Students performance may vary depending on study hours and tutoring hours before each exam. Should I center the predictors ...
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1answer
79 views

Imputation of missing data before or after centering and scaling?

I want to impute missing values of a dataset for machine learning (knn imputation). Is it better to scale and center the data before the imputation or afterwards? Since the scaling and centering ...
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2answers
323 views

The order of Data Centering and Data Transformation

Edit: I just read a related post (How to include $x$ and $x^2$ into regression, and whether to center them?) which mentions that centering a variable creates a new variable. However, as the comments ...
2
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2answers
168 views

Between-subjects effect becomes non-signicant after centering covariate. Should I center or not?

I've used a general linear model function to run an ANCOVA, involving a categorical predictor (with two levels), a continuous predictor, and their interaction effect. If I don't center the ...
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0answers
15 views

When should one centre variables in a cox proportional hazard model and when not? [duplicate]

I want to use a Cox proportional hazard model in order to analyze the prognostic value of a certain variable (I divided it in quartiles and so I have 4 categories) with respect to the time to event ...
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0answers
32 views

Is scaling data valid for Kruskal-Wallis test?

I have a dataset of fresh matter (FM) weights of salad measured in field over time (6 Dates, 40 Plants each). Those are measured independently, so at every date different plants were measured. As in ...
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1answer
30 views

Which mean to use for centering variables when sample definition varies

I am centering variables that enter interaction terms in my linear regression. To check the robustness of my results, I exclude certain cases from the original sample, and re-run the regression ...
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3answers
277 views

How to include $x$ and $x^2$ into regression, and whether to center them?

I want to include the term $x$ and its square $x^2$ (predictor variables) into a regression because I assume that low values of $x$ have a positive effect on the dependent variable and high values ...
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1answer
147 views

Do you ever center AND standardize variables in multiple regression?

Do you ever center AND standardize variables in multiple regression? It seems as if standardization would automatically center variables...is this true?
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3answers
1k views

Is centering a valid solution for multicollinearity?

Let's assume that $y = a + a_1x_1 + a_2x_2 + a_3x_3 + e$ where $x_1$ and $x_2$ both are indexes both range from $0-10$ where $0$ is the minimum and $10$ is the maximum. I found by applying VIF, CI and ...
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35 views

Centering variables before running PCA [duplicate]

I am learning about PCA, regarding PCA I need to know that given a dataset is it always necessary to use centering? what if I don't center the variables used in PCA?
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626 views

How does knnimpute of the preprocess function work?

I am new to R and I use a script I do not completely understand. It preprocesses a dataset for data mining. At one point, the data (stored in fil) should be ...
2
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1answer
998 views

Centering data in multiple regression

In a multiple regression analysis (with 4 continuous predictors and 2 categorical factors), we mean centered the data (for each continuous variable) due to issues of multicollinearity when the ...
2
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0answers
185 views

Which variables should I transform, center, and/or standardize in my data for Principal Component Analysis?

I have multiple datasets that I am attempting to use principal component analysis (PCA) on in order to infer the underlying structure of the data. I'm attempting to predict growth increment of ...
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2answers
59 views

Does it make sense to partially scale the data matrix X in regression?

For some reason my supervisor wants me to centre only the independent variables that are used in interaction terms. I have never heard of such a practice. Does it make sense to partially centre data ...
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1answer
1k views

Converting standardized betas back to original variables

I realise this is probably a very simple question but after searching I can't find the answer I am looking for. I have a problem where I need to standardize the variables run the (ridge regression) ...
3
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0answers
82 views

Should I de-mean a predictor variable before a dummy interaction

Suppose I have the following time-series linear model where $\beta$ is misspecified: $Y(t+1) = \alpha + \beta X(t) + \sum_{i=1}^{10000}\gamma_i Z_i(T) + \varepsilon$ where all parameters are in ...
7
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2answers
934 views

How to include a linear and quadratic term when also including interaction with those variables?

When adding a numeric predictor with categorical predictors and their interactions, it is usually considered necessary to center the variables at 0 beforehand. The reasoning is that the main effects ...
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2answers
131 views

Centering when using splines in R

I am having trouble understanding why centering seems to only work with simple linear models and not with splines for example. I am using centering to report the estimated group differences at ...
2
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0answers
155 views

Interaction Term Insignificant but Composite Variable Significant

I have 4 latent variables each with 3-7 indicators. I created a composite for each variable by summing the data and then mean-centering (variables have some collinearity issues, highly related). ...
4
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0answers
149 views

How to do centering if I have a quadratic term?

I have been trying to run a multilevel model with both a linear and a quadratic term for income as my main variables of interest. It looks something like: \begin{eqnarray} ...
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1answer
66 views

How to determine the best mean to use for a developmental comparison using z-scores?

The data contains two groups and the intended comparison will be completed via independent t-test. Options that I have considered is using the entire sample's mean or one of the group means. However, ...
11
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2answers
6k views

Why could centering independent variables change the main effects with moderation?

I have a question related to multiple regression and interaction, inspired by this CV thread: Interaction term using centered variables hierarchical regression analysis? What variables should we ...
5
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1answer
3k views

Interaction term using centered variables hierarchical regression analysis? What variables should we center?

I'm running a hierarchical regression analysis and I have some little doubts: Do we calculate the interaction term using the centered variables? Do we have to center ALL the continuous variables we ...
6
votes
1answer
517 views

Should I re-center variables when looking at moderator effect in men and women separately?

I want to see if an interaction variable in a multiple regression is significant for the whole sample, and then just for men and just for women. When I created the interaction variable for the whole ...
3
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1answer
88 views

Convert back standardized linear predictor

I guess this is a quite basic question, but I have been struggling with this for quite some time, so I hope someone can help me with this. I have a model (type is not relevant for now) which includes ...
3
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0answers
199 views

Interpretation of interaction term in Cox PH model when centering LP on mean values of predictors

Let's say I have a Cox PH model for predicting the risk of dying, that in a simplified form looks something like this: ...
0
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0answers
164 views

GEE: Pairwise comparisons at different levels of a covariate?

I'm familiar with basic regression methods, but have no experience using GEEs. I use SPSS, and I'm trying to use a GEE for a dataset that I have, because there is a repeated measures component in my ...
2
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0answers
65 views

Few main variables in the best model still show multicollineairty. Should I remove them despite their importance?

I have a binary logistic regression with 5 IVs and all of their 2-way interactions. I have reduced/removed multicollinearity between main variables and their interactions by centering the main ...
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1answer
202 views

After centering, interactions' effects got reversed. It was not fixed by reversing the dependent variable. What should I do?

In a binary logistic regression, I centered all the independent variables (binaries, continuous, dependent, independent, all [I have 5 IVs: three binary and two ordinal]). Multicollineariy was ...
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52 views

Centering to use a sparse covariate?

In my dataset, there's a binary response, some factors, and some covariates. In particular, there are some covariates that are always present when factor1=="A" and ...
11
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1answer
532 views

Is centering needed when bootstrapping the sample mean?

When reading about how to approximate the distribution of the sample mean I came across the nonparametric bootstrap method. Apparently one can approximate the distribution of $\bar{X}_n-\mu$ by the ...
4
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1answer
485 views

Shifting bootstrap confidence interval to be centered around original parameter

I've been doing a bit of research into bootstrapping as I've been told one method of performing it, and this seems to differ from what I can find in other sources. I have a sample, and want to ...