# Questions tagged [centering]

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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### Centering variables in Lavaan - Path analysis

I hope you're doing well. I'm currently knee-deep in path analysis using the lavaan package for my research. My analysis involves moderation, and centering the variables may simplify coefficient ...
22 views

### Methodology for Analyzing the GAP Between Provinces: Using Derived Variables and Considerations on Fixed Effects Regression

I have a panel data for 106 provinces and 10 year. I want to use a new variable created from the difference of any observation with the mean of the top 10 provinces (highest value), year by year. It ...
1 vote
32 views

### Show: scaling transformation $Y_i=D^{-1}(X_i-\bar{X})$ can be written as $Y = HX_{n\times p}D^{-1}$

Show that the scaling transformation $\textbf{y}_i=D^{-1}(\textbf{x}_i-\bar{\textbf{x}})$ can be written as $Y = HX_{n\times p}D^{-1}$ where $H$ is the centering matrix $(I_n-\frac{1}{n}\textbf{11}')$....
168 views

### How to decorrelate $X$ and $X^3$?

We know that if $X$ is positive, then $X^2$ is highly positively correlated with $X$. I've plotted an array of integer numbers from 100 and 110 with the following code: ...
16 views

### Centering a skewed predictor variable in a multilevel model that is involved in an 2-way interaction

Is there a correct method to center (mean or median centering) a skewed predictor variable in a multilevel model? The predictor is a skewed, count variable and will feature in a two-way interaction ...
26 views

### Within-subject mean centering of covariate in linear mixed models

I have a within-subject repeated measures dataset where participants were asked to rate images (48 items) at 3 separate time points (t0,t1,t2). Their ratings at t0 is what is defined as baseline, as ...
17 views

### About centering to accommodate multicollinearity (Ordinal Logistic Regression Analysis, Logistic Regression Analysis)

When interaction terms are used in multiple regression analysis, often centralization of the variables (subtracting the mean of the variable from each variable) is used to deal with multicollinearity, ...
19 views

### Scaling variables for model selection. Unscaling for final model?

I struggle with the following question: I had to scale variables for model selection as they were in very different units and the model struggled to converge. Now that I have a final model the ...
20 views

### Mean-centerinfg for logit values?

I have a question regarding the logistic growth model. Can proportion values that have been converted into logit be mean-centered? When we calculate the actual difference value between two proportion ...
225 views

### Does mean centering work only for normally distributed variables?

In econometric analysis in some cases, such as models with interaction terms, multicollinearity between independent variables may exist. In such cases, some researchers suggest "mean-centering&...
1 vote
75 views

### Interpreting interaction between a categorical and centered continuous variable (binary response)

In my model, in which I'm attempting to infer which covariates affect whether a fish has an empty stomach or not (1=empty, 0=not empty), I decided to grand-mean center the variable "SL" (...
118 views

### Using BayesFactor R Package Instead of P-Values in Mixed Modelling

I have been using lme4 in R to run a linear mixed effects model. ...
29 views

### Is it possible to complete a Time-Lagged Multilevel Model with time-variant predictors that change systematically with time?

I have a data set of 139 individuals who provided responses to a series of questionnaires at 5 times points (0, 3, 6, 12 and 18 months) across treatment. Time is included as a covariate in the model (...
1 vote
74 views

### Regression analysis with constant dependent variable

Can someone explain to me what's going on in the following? Suppose we have data with constant dependent variable: ...
59 views

### Which method to use to scale/mean center a time-varying covariate in latent growth models (SEM)?

I have longitudinal data across several time points. At each time point, participants completed an online test up to 3 times (i.e., measurements were completed 1-3 times at each timepoint). The number ...
7 views

### Centering outcomes using sample versus population means with baseline measures

Suppose longitudinal experimental data where outcome outcome $y$ is measured at baseline, units randomly receive a treatment or control condition, then $y$ is measured again. You fit the below model ...
62 views

### Dropping a hierarchical linear model intercept when centering the outcome at 0?

Suppose a hierarchical linear model with "random intercepts" $\mu_i$ fit to some raw (unscaled) data: $$y_i \sim N(\mu_0 + \mu_i, \sigma) \\ \mu_i \sim N(0,\sigma)$$ If I rescale $y_i$ by ...
51 views

### Centering Categorical Predictors in Mixed Models

Apologies if this is a repeat question; I couldn’t find another post that asked this specifically. I’m running a linear mixed effects model with a continuous outcome (reaction time) and categorical ...
1 vote
90 views

### Centering variables involved in an interaction changed results, how is this correctly interpreted?

In my model, some potentially confounding continuous variables had to be taken in account as well as an interaction of this variable with the main factor of interest, which is categorical. Initially, ...
430 views

### Why does mean-centering in a univariate logistic regression change p-values?

I have a very simple logistic model with a single continuous independent variable and a two-category dependent variable. When I mean-center the IV, the p-value of the coefficient changes significantly,...
12 views

### How can we develop good priors for group means when centering with unbalanced classes?

Suppose you have data on $y_i$, the outcomes from an experiment in which units were randomly assigned to be in a treated group ($z=1$) or a control group ($z=0$). Let's further assume each group's ...
1 vote
23 views

### Is there a "proper" way to keep strictly nonnegative data nonnegative when performing PCA, despite centering?

I have a question that came up in my research and I would really appreciate some guidance from someone wise in the ways of dimensionality reduction. I have a dataset of matrices that are strictly ...
46 views

### How does center variable help address multicollinearity problems for interaction with polynomial terms

I hope someone can help me better understand how center variables can help address the problem of multicollinearity problem when the regression includes interactions with polynomial terms. My ...
75 views

### How do we report a regression with categorical * continouns interaction?

I was wondering how would be the best way to report this model ? ...
559 views

### What does "1-unit change" mean when centering predictors in regression?

I know that when we standardize a predictor, "one unit change" becomes one standard deviation in the predictor, but what if we only center the data on the mean (i.e. only subtract all values ...
63 views

### Both quadratic and linear term are insignificant

I am trying to fit a model which has age as a control variable and mental health score as my dependent variable. I centered the age because 0 is not meaningful in my analysis. I tried age, age^2, log(...
1 vote
153 views

### How to obtain uncentered factor scores from Factor analysis

The Exploratory Factor Analysis has the following mathematical formulation as in the screenshot from wikipedia (https://en.wikipedia.org/wiki/Factor_analysis): That means the factors in F are ...
25 views

### Centering predictors in linear mixed effects and explaining three-way interactions with continuous variables [duplicate]

I am working on a Linear Mixed Effects model. All four predictors are continuous variables. Full model: ...
181 views

### centering issue in the multilevel modeling

I learned that categorical variable should be centered just like continuous variable. I am analyzing two level model, (MLM). case 1. when the categorical variable is level 1 predictor, and have ...
215 views

### Mahalanobis vs centering / standard deviations

Is there a difference whether to use a Mahalanobis distance or transform the data via centering (and normalization) when you are interested in calculating distances? This means, if you are interested ...
181 views

### What does it mean if we use eigenvetor matrix of centered matrix $\mathbf{X}$ to reduce the dimension of $\mathbf{X}$ without centering?

Recently, I was trying to use PCA to reduce the dimension of matrix $\mathbf{X}$. Suppose a data matrix $\mathbf{X}\in \mathbb{C}^{M\times N}$, where $M$ is the number of variables and $N$ is the ...
477 views

### "Group mean centering" a dummy Variable in R for multilevel analysis: how can i do this?

have somebody an idea of how to group mean center a dummy Level 1 predictor in R? Enders & Tofighi (2007) describe a method to center a dummy variable through substracting the proportion of the ...
281 views

### PCA whitening and centering in inference/test samples

[cross-posted from SO] I'm working on speaker identification. I need to take the speaker embeddings from a neural network and apply a few transformations to finally generate the score for verification....
1 vote
533 views

### Centering variables that use Likert scales..?

I'm running a moderation analysis, and I was taught that you should center all continuous independent variables. In my department, professors usually treat variables that use Likert scales as ...
201 views

### How does group mean centering affect the interpretation of coefficients in a hierarchical model?

I've dived deeply into the literature, but still don't understand if it's necessary to group-mean center my predictors if I'm entering them into a hierarchical model. Surely, if they're being entered ...
15 views

### original mean from centered array

Given the mean-centered array a <- c(-2.25,0.75,-1.25,2.75,-0.25,1.75,-0.25,-1.25) is it possible to retrieve the mean of the original array used to center it ...
1 vote
284 views

### When is ok not to centre the data before using it in PCA?

I want to find out if it is ok not to center the data in a PCA when working with stock returns. Centering would remove the trend from the dataset which I believe contains valuable information. The ...
98 views

### Can I GROUPMEAN center one variable and not the second one involved in an interaction / Multilevel Model with L1 Moderation

I'm fitting a multilevel model with an L1 moderation on Mplus. I am trying to demonstrate that the effect of X (independent variable / mean of scale items) on Y holds only when people do not make a ...
1 vote
100 views

### Cosine similarity with recentering - collaborative filtering

I don’t know much about stats (nor maths), so I’m sorry if I’m not being very clear on this... I’m trying to build a simple recommender system for books using collaborative filtering item by item. I’...
1 vote
17 views

### Problems with 0s when centering a dummy variable within cluster

Supposing that I have a set of data that is structured like this: customerID orderID couponUse purchaseQuantity 1 1a 1 3 1 1b 0 1 1 1c 0 1 2 2a 1 5 2 2b 1 2 3 3a 1 6 3 3b 1 3 3 3c 1 7 3 3d 1 ...
1 vote
201 views

### Centring in three levels multilevel models with cross-level interaction

I am relatively new to multi-level models subject and find it challenging to connect theory to modelling. My interest is to examine the moderation influence of green space (at level 3) on the ...
1 vote
326 views

### Linear Mixed Effects - degenerate Hessian with 1 negative eigenvalue

I am using linear mixed effects to look at how the variable Neuro (measured at baseline only) predicts change over time in the variable Score (measured at baseline, visit 2 and for some participants ...
198 views

### Group centering for interactions with within-between mixed panel model

I need to update a model to incorporate an interaction between a time-invariant categorical variable and a demeaned time-variant variable. I'm unsure about how to correctly use group-mean centering ...
192 views

### Why does centering variable A influence my p values of factor B in the linear mixed effects model?

I have a dataset, where I would like to see whether there is a group difference in the measurement "concentration". I have repeated measurements for some subjects, which is why I use a mixed-...
1 vote
27 views

### Whats the motivation to demean variables when estimating an interaction effect? [duplicate]

I am trying to estimate a regression model where I am interested in the effect of a certain magnitude, probability and expected value (probability * magnitude ) on reaction times. I was told that it ...
986 views

### Mean-centering variables in glmer

I have the following model in r that compares the differences between dives where whales fed and dives where whales didn't fed (distribution is binomial: presence of feeding (foraging) = 1, abscence = ...
1 vote
122 views

### Why does centering NOT cure multicollinearity?

In several posts, such as Is centering a valid solution for multicollinearity?, it states that centering doesn't solve multicollinearity because "it's a linear transformation." I just made ...
287 views

### Applying de-standardised ridge regression coefficients to new test data - how to best handle the mean of y_test?

this is my first post on Stackexchange, so please correct me in any way if I am doing it wrongly. I just stumbled across this question, I was battling with the same issue, but the posts there ... 1 vote
Suppose that we have the following model $Y = b_{0}+b_{1}*Season +b_{2}*Income$ In order for $b_{0}$ to refer to the expected value of $Y$, we should center the variables Season and Income. However,...