The residuals of a model are the actual values minus the predicted values. Many statistical models make assumptions about the error, which is estimated by the residuals.
2
votes
1answer
26 views
What does it mean to correlate residuals in SEM?
I have been reading a paper by Cole, Ciesla, and Steiger, which argues in many cases allowing residuals to correlate is justified. However, I am not entirely sure what it means for residuals to ...
1
vote
0answers
46 views
How to interpret negative factor loadings and residual variances in SEM?
I've been trying to fit a SEM model, using misconceptions and the correct conception as latent variables.
My instrument is a set of items that ask a binary yes or no question. (Is something in a ...
0
votes
1answer
92 views
Does this histogram of residuals indicate that the residuals are effectively random?
I am studying a univariate and discrete time series. I know that residuals should be effectively random and have a good fit, and should have a bell shape.
Does the plot below suggest that the ...
6
votes
1answer
109 views
What does the residual higher level variance tell me?
I have a multilevel logistic regression model predicting the probability of item nonresponse, where the random intercept variance at country level takes on the following distribution for the different ...
0
votes
0answers
22 views
Modelling a skewed, 10-point Satisfaction variable
I am trying to replicate and hopefully improve on an analysis done in a study to find determinants of patient satisfaction after shoulder surgery. Satisfaction is heavily skewed (with over 60% of ...
1
vote
1answer
384 views
What is residual standard error?
When running a multiple regression model in R, one of the outputs is a residual standard error of 0.0589 on 95,161 degrees of freedom. I know that the 95,161 degrees of freedom is given by the ...
4
votes
1answer
68 views
Interpreting a residuals vs fitted plot and extracting points
I'm doing a multivariate linear regression with R, and i find myself with the following residuals vs fitted plot:
As you can see there is a very regular line of points that seems to follow a ...
2
votes
2answers
79 views
What is the expected distribution of residuals in a generalized linear model?
I am performing a generalized linear model, where I have to specify a family different from the normal one.
What is the expected distribution of residuals?
For example, should the residuals be ...
1
vote
2answers
112 views
How to calculate the regression variance for a GLS model?
I need to calculate the regression variance ($\sigma^2$) in order to estimate both the confidence intervals and the prediction intervals in a gls regression analysis. For the analysis, the covariance ...
4
votes
0answers
52 views
Hierarchical regression using residuals
Edit: Perhaps my first asking (see below) was a little too ambitious. The crux of the question is this: in a linear regression setting, is there anything statistically invalid about regressing the ...
0
votes
0answers
62 views
Autocorrelation in Residuals for VAR model
I am making some macro three-variable VAR models in R, where one of my models have autocorrelation in the residuals, as tested by a B-G LM test.
The two models are:
...
0
votes
1answer
62 views
Confusion about error term in ARMA-model when predicting future values
Let's say I'm fitting data for example to ARMA(1,1)-model:
$x_t = \phi x_{t-1} + \epsilon_t + \theta \epsilon_{t-1}$.
Now I estimate the parameters $\phi$ and $\theta$ and solve some values for ...
2
votes
1answer
81 views
How to extract/compute leverage and Cook's distances for linear mixed effects models
Does anyone know how to compute (or extract) leverage and Cook's distances for a mer class object (obtained through lme4 ...
4
votes
0answers
57 views
Residual from Functional Demographic model for fertility
I'm trying to fit a functional demographic model (fdm) to fertility rates using the demography package in R. When I've plotted ...
4
votes
3answers
157 views
What do normal residuals mean and what does this tell me about my data?
Pretty basic question:
What does a normal distribution of residuals from a linear regression mean? In terms of, how does this reflect on my original data from the regression?
I'm totally stumped, ...
0
votes
0answers
51 views
How can I manually calculate Score and Schoenfield residuals for a coxph fit in R?
I am trying to develop a solid understanding of Martingales and various survival residuals calculated using Martingales. To do that, I am attempting to explicitly calculate them for the below dataset ...
1
vote
2answers
163 views
Standardized residuals in R's lm output
I have a quick question: if I plot the diagnostic plots to an R regression, a couple of them have "Standardized Residuals" as their y-axis such as in this plot:
My question is this: what are the ...
2
votes
2answers
73 views
Summary of residuals in R
Disregarding "Deviance" in the image, the output of multiple regression analysis in R looks pretty much like this.
As far as I understand, residuals are errors. Do the 5 value summary refer to ...
3
votes
1answer
107 views
QQ plot is consistent with normality when subgroups are non-normal
I have read that for a one way ANOVA, you should check that the model residuals are normally distributed. If the variance of each group is homogeneous then this implies that the residuals with each ...
2
votes
1answer
43 views
Explanation of a step in derivation of residuals for R lm diagnostic?
I'm reading Faraway's book (http://cran.r-project.org/doc/contrib/Faraway-PRA.pdf) to try to understand R's lm diagnostic plots. On page 72 of the book is this:
I have been trying to understand a ...
3
votes
1answer
130 views
ANOVA:How to detect non-normality with a QQPlot in the presence of non-homogeneous variance
This is a pretty general question but, I often find statistical textbooks claiming that, in order to justify the within groups normality assumption of a one way ANOVA, you can look at a QQ plots of ...
0
votes
0answers
56 views
finding the residual variance after correcting ordinal data for sex
I have a data set organized as: males, females as groups. Each individual has a "score" that is ordinal, ranking 0,1, or in another case, 0,1,2.
I need to find the residual variation after correcting ...
0
votes
0answers
87 views
Question about the validation step for a multinomial logit model
I've been skimming through a couple of books (all german ones, hence I do not cite them here) at what residual plots one should look at if the usual model assumptions in the context of a multinomial ...
0
votes
0answers
56 views
Which of the three residual plots shows the most evidence of a possible violation of any of the linear regression assumptions?
https://www.dropbox.com/s/a6oojun3rkvv9a6/Screen%20Shot%202013-01-25%20at%2011.53.07.png
https://www.dropbox.com/s/losw1w0raojq2he/Screen%20Shot%202013-01-25%20at%2012.09.06.png
Which of of the ...
0
votes
0answers
52 views
Forecasting volatility using HAR-RV, residuals are greater than predicted value
I have tried using the following model (HAR-RV) to forecast volatility:
...
2
votes
1answer
183 views
Checking normality of residuals in 2x2 mixed methods ANOVA
I am running a 2x2 mixed method ANOVA (with one between-group factor and one within-group factor - time 1 and time 2). I want to check whether the assumption of normality of residuals is met. When I ...
3
votes
2answers
159 views
Troublesome residual plot from linear mixed model
I have fitted the following linear mixed model based on the results of an economic game:
lmer(TotalScore~perOOgivenP+Game+(1|Subject),REML=T,data=mdl1table)->m1
...
1
vote
1answer
75 views
residualize binary outcome variable
Does it make sense and what is the correct approach to residualize a binary variable? For a continuous variable y, I simply run a regression that predicts ...
1
vote
1answer
185 views
Pearson residuals formula in a multinomial logit model
Could someone tell me what's the formula for the Pearson residuals in a multinomial logit model?
I tried to look for it but I haven't found anything.
6
votes
2answers
318 views
Influential residual vs. outlier
First, I should state that I have searched on this site for the answer. I either didn't find a question that answered my question or my knowledge level is so low I didn't realize I already read the ...
2
votes
1answer
118 views
What is an appropriate formula for residuals calculation in a model describing a single-factor repeated measures design?
For the repeated measures design D.C.Montgomery in his "Design and Analysis of Experiments" book provides the mathematical / statistical (linear) model: $y_{ij} = \mu + \tau_i+ \beta_j + ...
0
votes
0answers
31 views
Reasons for fitting results (anti image)
I need to interpret a residual table which was fitted by an analyst plotting $y_.0123$ (final residual) against the $x_{1.023}$. The table represents residuals produced by each variable.
...
8
votes
4answers
631 views
Why squared residuals instead of absolute residuals in OLS estimation?
Why are we using the squared residuals instead of the absolute residuals in OLS estimation?
My idea was that we use the square of the error values, so that residuals below the fitted line (which are ...
4
votes
2answers
143 views
Does a zig-zagging residual plot mean that normality has been violated?
I have the following diagnostic plot for my data. Is normality violated, especially given the zig zagging residual plots?
2
votes
0answers
519 views
Pearson's residuals
A beginner's question about the Pearson's residual within the context of the chi-square test for goodness of fit:
As well as the test statistic, R's chisq.test ...
2
votes
1answer
130 views
Should raw data or residuals be used to check homogeneity of variance?
Unexpectedly for me (!) I've recently learnt that:
"We have assumed that the error terms, $\epsilon_{ij}$, of the variates in each sample will be independent, that the variances of the error terms ...
2
votes
1answer
69 views
RMS error of the SD line
Freedman's Statistics (p. 147 of the hardcover edition) says that if $Y$ is estimated using the SD line (rather than the regression line) then the RMS error of the residuals is ...
2
votes
1answer
594 views
Deletion residuals
Please can you help me to solve this problem. It should be calculated by vectorization. The question is:
The i-th deletion residual $e_{(-i)}$ is defined as $e_{(-i)} = y_i - X^\top B_{(-i)}$
...
-4
votes
2answers
254 views
What does it mean in terms of regression if residuals are not white noise?
I need help in answering this one, it is an exam question.
4
votes
2answers
338 views
What advantages do “internally studentized residuals” offer over raw estimated residuals in terms of diagnosing potential influential datapoints?
The reason why I ask this is because it seems that internally studentized residuals seem to pattern the same as raw estimated residuals. It would be great if someone could offer an explanation.
2
votes
0answers
129 views
How to fix the constant variance assumption?
We have a project where we have to find the best model using a large set of data. In our current model there are 10 variables, some quantitative, and a few that are qualitative. When we first do ...
1
vote
0answers
253 views
Estimate of sigma squared in a simple linear regression when H0: beta = 0 is true
I was reading some lecture notes on simple linear regression where one section said that when the slope is 0 (hence, H0: beta = 0 is actually true), (SSY - SSE)/(DFY - DFE) estimates sigma squared. ...
1
vote
1answer
77 views
Model simplification results in non normal residuals
I have a data set that includes a response variable (counts), two categorical explanatory variables, and one covariate.
The response variable being counts, I ran a GLM with poisson distribution, and ...
1
vote
0answers
59 views
Estimating fixed effects for ordinal regression
I am running a model when the response variable (behaviour) is an ordinal factor (levels: 0,1,2,3,4) and I am testing the relationship with two fixed effect factors (year: A,B,C,D; colony; X1,X2).
I ...
1
vote
2answers
230 views
Does the sign of the adjusted residuals matter in a crosstable?
In a cross table, if the adjusted residual value for a cell is less than -1.96 or greater than 1.96 then we could say that this cell is determinant in the dependency (suppose pearson is 0.03). ...
5
votes
2answers
133 views
How to understand the square of an AR(1) process?
I generate an AR(1) process as follows:
x=arima.sim(list(order = c(1,0,0),ar=0.67),n=1000,sd=sqrt(0.55))
When I square it, and fit AR(1) to the squared process, ...
2
votes
0answers
125 views
Statistical test for whether a process is a red noise
We know that red noise is the same as a first-order autoregressive (AR(1)) stationary Gaussian process with a positive correlation at unit lag. Does there exist some formal statistical test for red ...
3
votes
0answers
208 views
Simultaneous heteroscedasticity and heavy tails in a regression model
I'm trying to create a prediction model using regression. This is the diagnostic plot for the model that I get from using lm() in R:
What I read from the Q-Q plot is that the residuals have a ...
2
votes
0answers
46 views
Transformation optimizing stationarity of the residual of a regression
I am trying to define an objective function or a method to find the transformation and coefficients optimizing the stationarity of regression's residuals.
For instance, if I want to regress $X_1$ vs ...
2
votes
1answer
322 views
How can we get different mean and median values for residuals when working with the same dataset?
Following this R instruction
> fit <- lm(spending ~ sex + status + income + verbal, data=spending)
I would like to calculate the mean and median of the ...
