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.

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48 views

Why do normal-pseudo residuals measure the deviation from the median?

I have read this and I have stuck on page 4. It says that By definition [a normal pseudo-residual] is precisely $N(0,1)$ distributed and its value is zero if $Y$ is equal to the median of its ...
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25 views

What is a good way to know if a variable adds value to an existing regression model without its components

Suppose someone gives you the fitted values to a regression model with $k$ terms, along with the fitted coefficients. If this is all you have, and you are investigating an additional "term" or set of ...
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24 views

Comparing importance of features in different datasets in GLM

I want to compare the importance or 'predictive power' of the same feature in 2 different datasets. Specifically let $[\bf{y}_1,\bf{V}_1]$ be my output & design matrix of dataset 1 & $[\bf{y}...
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18 views

Deviance residuals in Cox Model

Based on this article: Click here, the martingale residuals is a sum of each martingale residual per subject from counting process data. So, if deviance residuals in Cox regression are defined by: $$...
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1answer
30 views

Standard error of residuals v.s. standard error of regression

We know that in simple linear regression the variance of the regression error, $\sigma^2$, is estimated by $\frac {\sum_{i=1}^{n} (y_i - \hat y)^2} {n-2}$, i.e., the Mean Squared Error of the errors. ...
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1answer
27 views

Chosing the right test for weekly disease counts

I am using STATA to analyze count data (weekly disease counts), and I am trying to pick the best test between Poisson, negative binomial and zero-inflated Poisson / negative binomial but I am not sure ...
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75 views

If I do a robust regression using standard error, what do I need to analyse in the residuals

Let's say I do a multiple regression, using robust (Stata option). It is a robust standard error regression. I want to analyse and discuss residuals. Residuals versus fitted values Is it ...
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16 views

Assess the model of Multinomial Logistic Regression

Some people told me that AIC and residual deviance are good statistics to assess multinomial logistic regression model. But I don't know how to use it in multinomial logistic regression. Anyone here ...
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12 views

Using raw residuals rather than standardized residuals for Q-Q/P-P plot and residual vs fitted plot

When I was doing my undergraduate studies, I remembered that my lecturers usually uses raw residuals to obtain the plots mentioned above. Some books that I have also used raw residuals. However, ...
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40 views

Residuals with glm / glmer don't have null mean

I am trying to fit accuracy data (taking values 0 or 1) using glmer and I am puzzled to observe that the residuals of the model don't have a null mean. Wasn't this the whole point of the optimization.....
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33 views

How to interpret regression diagnostic plots for multiple linear regression analysis (with specific example)

I recently using the day.csv file which is downloaded from http://archive.ics.uci.edu/ml/machine-learning-databases/00275/ to build a regression model for the last column “cnt” in R. This is the ...
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9 views

type 1 and type 2 errors for non-normal residuals in a regression

I did a regression and performed a normality tests on my residuals, which reject the Null Hypothesis that the residuals are normally distributed (the true distribution seems to be flatter with fatter ...
2
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1answer
76 views

t-Test residual analysis

I'm reading Experimental Design and Analysis by H.Seltman (http://www.stat.cmu.edu/~hseltman/309/Book/Book.pdf) and working on the provided HCI dataset (SPSS format, can be downloaded from page 143). ...
0
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1answer
20 views

Time Series Modelling[Issue with modelling the residuals]

I am doing the sales forecast. I found the trend and seasonality manually for my time series data. Regressed time series data against the trend and seasonality and found the residuals. The residuals ...
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0answers
36 views

How to improve the fit of a zero-inflated, negative binomial glmmADMB model

I have been trying to fit count data that is zero-inflated and overdispersed using generalized linear mixed models. My research led me to the glmmadmb function in the glmmADMB package. I am fitting ...
2
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1answer
27 views

What does excessive correlated residuals (as indicated by modification index) say about a model?

This question/post is a follow-up to a few previous posts so please forgive the redundancy. My question is what excessive number of modification indices suggesting high number of correlated errors ...
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22 views

Linear mixed model with skewed residuals

I have a dataset of 720 observations, 15 each on 12 sites and in 4 points in time. My aim is to find out if there are differences in the measured variable between the sites and times of measurement. ...
0
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41 views

errors in the orthogonal factor model

I am using R psych package in order to design a factor model. By default, an oblique rotation (oblimin) is performed by fa. The number of factors (fa.parallel$nfact) has been previously estimated. <...
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1answer
24 views

What to do with a linear regression model with non-normal residuals and evidence of seasonality?

Assuming I already have an existing linear regression model: $y(t) = a + bx(t) + e(t)$, where: $a$ & $b$ are the constant coefficients $e$ is the model residual error $t$ denotes time You've ...
0
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1answer
16 views

Residuals of SARIMA follow Student's $t$ distribution - implications?

I have fitted a SARIMA model to my time series. The diagnostics of the residuals are all good (ACF, PACF, ...), i.e. it seems they behave like white noise. But when I plot the normal qq-plot, they ...
0
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1answer
31 views

Regression analysis and how to assess the assumption of normality of Y

I was told that to assess normality of Y in a regression, it is better to look at the residuals, rather than the conditional distribution of Y for each given X. My understanding is that both are ...
0
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1answer
16 views

Show that the adjusted values for 2x2 tables under the assumption of independence have the same absolute value

I am trying to show that, for 2x2 tables, under the assumption of independence, that all four adjusted residuals have the same absolute value. Adjusted residual: $r_{ij}=\dfrac{n_{ij}-\hat{u_{ij}}}{\...
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10 views

Goodness of fit for complex valued curves (i.e. frequency responses in frequency domain)

I'm not a hero at statistics, som my apologies for perhaps the stupidity of this question. Presume that one has the frequency response $Y_{data}(k)$ and also has the synthesized response $Y_{syn}(k)$. ...
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1answer
54 views

Residuals as indication of transformation of data

In R I have data and I want to make a regression analysis, finding a function that can fit the data. So head(data) gives ...
4
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1answer
36 views

$Y=\epsilon$ in GLM?

In general linear model $$Y=X\beta +\epsilon $$ the LSE for $\beta$ is $$\hat \beta=(X^TX)^{-1}X^TY$$ and so $$\hat Y=X\hat \beta=X(X^TX)^{-1}X^TY=HY$$ where $H=X(X^TX)^{-1}X^T$. Then the ...
3
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1answer
34 views

Do points with high Cook's distance necessarily have a high standardized residual, and vice-versa?

I have two questions below: Could a data point be an influential point if its cook distance is outstanding(greater than 4/(n-p-1)) while its standardised residual is less than 2? It looks like to me ...
0
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1answer
38 views

If my data follows a normal distribution, does that mean my residual are normally distributed as well?

I have a data set which approximately follows a normal distribution. Does that necessarily mean that the residuals (as define) here) of my dataset do follow a normal distribution?
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24 views

Cox-Snell residuals for Cox model with time varying coefficient

I am using the time transform feature of the coxph function in the survival package to model the effect of a time varying ...
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27 views

Evaluating hetroskedasticity in a binomial residuals vs. fitted plot in glmer?

I am trying to validate the goodness of fit of a model in glmer using residuals plotting. I went through many threads here related to this but still I am not sure that the solutions offered apply to ...
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1answer
30 views

Residual Analysis and ANOVA Model

I am very new to residual analysis and ANOVA. To my understanding, in the residual plot, residuals should not show obvious patterns, thus if the pattern is random, it indicates a good fit for a linear ...
0
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0answers
15 views

Poisson regression residual analysis

In a three factor poisson (log-linear) model $(A*B*C)$, when the highest interaction term $(A:B:C)$ is dropped, the response/raw residuals are exactly the same for different levels of two of the ...
3
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23 views

Linear regression with trimmed data

I would like to know how experts deal with real data. Even if statistical text books uses real data I'm always surprised how good the real data are and at the end of the exercises the residuals are ...
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1answer
46 views

Are these diagnostic plots from lmer too far away from normal and showing heteroscedasticity?

I have read similar posts in this website to help me assess whether my diagnostic plots are too far away from normal and if they are showing heteroscedasticity (Interpretation of residuals vs fitted ...
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13 views

Unbalanced binary features in LASSO regression

I have a target $y$ that I want to predict from variables $x_1, x_2, \ldots x_k$. Suppose the first of these variables, $x_1$, is a binary variable (i.e., only taking on one of 2 values). If I use ...
0
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0answers
16 views

normal distribution histogram of the residual from a simple regression model?

why residual histogram will follow a standard normal distribution? because independent variable can be different values, I can see all obersavations at one certain X value will follow normal ...
0
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0answers
20 views

Jackknife residuals formula

I know that the jackknife residuals are $$t_i={y_i-\hat y_{(i)}\over \hat \sigma^2_{(i)}(1+x^t_i(X^t_iX_i)^{-1}x_i)^{1/2}}$$ But there is alsa a formula for computing these residuals: $$t_i=r_i({n-p-...
1
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1answer
74 views

Does this residual plot indicate heteroscedasticity?

These are two versions of the same residual plot, just with a different scales, (I'm not sure which is easier to interpret so I included both). I don't need to know major details (for the assignment ...
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0answers
53 views

Residual network dimension changing blocks identity function

In trying to implement ResNet with bottleneck blocks for myself, I got very confused about the identity function residual blocks with different dimensions. They compared identity, conv projections on ...
1
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1answer
23 views

calculate the internally studentized residual

it says that ...an ordinary residual divided by an estimate of its standard deviation $s(e_{i})$ As we can see from the example that mean for four residuals is 0, so $s(e_{i})=\sqrt{\frac{(-0.2-0)^2+(...
1
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1answer
46 views

variance decreases when x gets farther from the average x?

I just read the description of Studentized residual on Wikipeida. I'm confused about what it says about variance, it says that "the residuals, unlike the errors, do not all have the same ...
0
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1answer
75 views

Differentiating the RSS w.r.t. $\beta$ in Linear Model

I am reading the book "The Elements of Statistical Learning". The book says But when I try to prove it, I get the following: $$RSS(\beta) = (y - X\beta)^T(y-X\beta)$$ $$RSS(\beta) = y^Ty -\beta^TX^...
0
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1answer
15 views

Absolute Average deviation in percentage calculation

Sorry if my terminology is incorrect. I am trying to calculate the average error of prediction to be represented in percentage. For example, I should be able to say, the predicted values are on ...
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19 views

is normality of raw data ever important? [duplicate]

http://www2.psychology.uiowa.edu/faculty/mordkoff/GradStats/part%201/I.07%20normal.pdf https://pubs.er.usgs.gov/publication/5224239 The two links above seem to me to claim the opposite. Is normality ...
0
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0answers
25 views

What does Tukey Test's p-value means in residual plot analysis?

After having called the residual plots command in order to graphically analyse residuals, I obtain also a written output where I can find the p-value and Test stat associated to each independent ...
4
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0answers
91 views

How do bottleneck architectures work in neural networks?

We define a bottleneck architecture as the type found in the ResNet paper where [two 3x3 conv layers] are replaced by [one 1x1 conv, one 3x3 conv, and another 1x1 conv layer]. I understand that the ...
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38 views

How to standardise linear regression

I have a set of death rates (that range from about 0.1 to 0.5), a set of body weights (that range from about 2 to 80), and I want to calculate standardised residuals for the death rates after ...
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1answer
19 views

Why square root for RSE?

Why should we put square root to get RSE ? what for?
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36 views

Why divide RSS by n-2 to get RSE?

Context: Simple Linear Regression, an intercept and a slope I have 2 question regarding this issue. Why should we divide RSS ? Why the divisor should be n-2, not n or n-1 ?
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1answer
37 views

Analyzing bad lm plots in R (Two parallel lines in Residuals and Normal QQ)

I am working on some stock analysis that I picked up to help me learn more about modeling. I have become comfortable analyzing these plots when they are more as expected but I can't figure out why ...
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36 views

Why are principal components of the residuals from a multivariate regression correlated with the estimated coefficients?

Say I have some data that follows a general linear model: $$ Y = XB + E $$ for which: $Y \in \Re^{n \times m}$, $X \in \Re^{n \times p}$ and $B \in \Re^{p \times m}$ Further, let's assume (1) that ...