There is a common understanding that, in many cases, the absence of extreme values (univariate outliers) in individual variables may reduce the likelihood of extreme values when considering multiple variables simultaneously (multivariate outliers).
May i get some good citations to strengthen above fact?
You can cite chapter 3.02: Regression Diagnostics of the Comprehensive Chemometrics book. The source and diagnosis of outliers is discussed there.
Univariate and multivariate outliers are two types of outliers commonly encountered in statistical analysis.
1. Univariate Outliers: Univariate outliers refer to observations that are extreme or unusual in a single variable. In other words, they are data points that deviate significantly from the rest of the data in a single dimension. Univariate outliers are identified by examining the distribution of a single variable in isolation, without considering the relationships with other variables.
For example, let's consider a dataset of students' ages. If the majority of students have ages between 18 and 22, but there is one student who is 40 years old, that individual would be considered a univariate outlier because their age deviates significantly from the rest of the dataset.
2. Multivariate Outliers: Multivariate outliers, on the other hand, involve observations that are unusual or extreme when considering the relationship between multiple variables. Multivariate outliers cannot be detected by examining the variables individually; instead, they are identified by considering the joint behavior of multiple variables simultaneously.
For instance, imagine a dataset with two variables: income and education level. If most people in the dataset have a moderate income and education level, but there is one person with a high income and low education level, that individual may be identified as a multivariate outlier because their combination of income and education differs significantly from the rest of the dataset.
In summary, univariate outliers are identified based on extreme values in a single variable, while multivariate outliers are identified based on the unusual combination of values across multiple variables. Detecting and handling outliers is an essential step in data analysis as they can affect the results of statistical analyses and models.
Hettiarachchi H.A.H. , what's your purpose in this ?
I think it makes sense that if there are fewer univariate outliers, the chance of there being a multivariate outlier would decrease --- all things being equal. But it makes sense to look for outliers in the variable space you're investigating. If it's a multivariate space, then it makes sense to look for the outliers in this space.
... I'm just wondering if you're looking to support an idea that isn't really the best approach. Maybe for theoretical reasons. But that may not be ideal in a practical approach ?
I agree with Sal Mangiafico's assessment of Dursa Hussein's response. It sure does look (and walk and quack) like AI generated text.
Hettiarachchi H.A.H., I don't recall ever seeing empirical data about the relationship between presence of univariate outliers and the presence of multivariate outliers. But I am (presently) far from convinced that there is a strong relationship between the two. Why? Because a multivariate outlier can be thought of as an odd combination of values. When explaining this to students, I give an example of a dataset that has demographic variables on a sample of people ranging in age from early childhood to old age. In such a dataset, ages of 5 and 85 would not be univariate outliers; and body weights of 20 kg and 95 kg would not be univariate outliers. But an individual with age = 5 years and body weight = 95 kg would be a bivariate outlier. Imagine what such a data point would look like in a scatter-plot.
Again, I have not seen empirical data on this question, but I do know that multivariate outliers can occur when there are no univariate outliers. HTH.
Copyleaks also classifies Dursa Hussein 's response as AI generated. It doesn't even answer the question (somethings to cite).
Bruce Weaver , is that example a veiled Canadian attack on the U.S. ? ;)
Daniel Wright , Yeah, it's exactly at the level of the Voight-Kampff test. But it would be nice if people took even the time to try to get the answer to address the question.
Bruce Weaver , I seem to remember Canadians talking about their 2nd Amendment gun rights, so yeah, you might as well take the 5th as well. ... I don't recommend adopting the whole U.S. Constitution, however, but that's another discussion...
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