Summary
Summary Multivariate Statistics
- Course
- Institution
Samenvatting of all colleges
[Show more]
Seller
Follow
daniekklijn
Reviews received
Content preview
Multivariate statistics – 1ZM31 – Q1 2021/2022Assignment 1
Data exploration
What is a multivariate data set? several variables are
measured for each unit of analysis
Notation: q variables q>1, n units of analysis
The data fit in a rectangle, rows/individuals can be shuffled
and columns/variables can be shuffled
Nonmetric data
Nominal scales: no ordering
- Dummy variables 0/1: e.g. EU citizen yes/no
- Categorical variables
o E.g. nonbinary/female/male
o E.g. country,
transportation (bike,
foot)
Ordinal scales: ordering
- E.g. education: primary
school, high school,
university, PhD
Metric data
Interval scales: no meaningful absolute zero
- E.g. temperature: 10C is not twice as hot
as 5C
Ratio scales: meaningful absolute zero
- E.g. the height of a person, the number of
employees
Data visualization
Boxplot: best to visualize metric data
Scatterplot: combined visualization of two metric
data variables
In this graph
- No correlation (check if this is significant)
- No causal relationship
1
, Why we care about outliers: an outlier is a data point that is very different from other data
points
Therefore
1. Outliers might indicate an error in
the data collection, or might be
unrepresentative of the population
(substantive concern)
2. Outliers have a disproportionate
influence on statistical analyses
(practical concern)
Results of the factor analysis are stable,
whether or not we exclude data points
with highest values of the MD
Multivariate outliers: Mahalanobis
distance (MD)
- Identify the center of the data
- Draw ellipse around the center of the data
- Each data point on the same ellipse has the same distance to the center
- A higher MD tells you that the data point is further away from the center of the data
- If the data is normally distributed then we know the distribution of the Mahalanobis
Distance
What if the data are not normally distributed?
- We cannot use the rule-of-thumb
- Outliers still have a large Mahalanobis Distance
- Go look into the data whether this is a valid data point
o Error in the data?
o If no error in the data, influence on the results?
Normality
QQ-plot: plot the observed quantiles against the theoretical
quantiles of the normal distribution
- If the data are normally distributed, then the sample
quantiles are close to the theoretical quantiles
- Look whether the data points are close to the 45-degree
line
- If they are not do a logarithmic transformation
2
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller daniekklijn. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $5.89. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
67474 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now