would you have survived the sinking of the titanic? webinar.pdf · sinking of the titanic •...
TRANSCRIPT
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Would you have
survived the
sinking of the
Titanic?
Presented by Dr. Neil W. Polhemus
Using the Statgraphics mosaic charts, multiple correspondence analysis and logistic regression procedures.
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RMS Titanic
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Sinking of the Titanic
• Struck an iceberg on April 14, 1912 and sank the
next morning.
• Carried over 2000 passengers and crew, many
of whom did not survive.
• Controversies have centered on the lack of
sufficient lifeboats and the differential treatment
of individuals based on class of accommodation.
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Sample Data File #1
Source: Robert J. MacG. Dawson, Saint Mary’s University http://www.amstat.org/publications/jse/datasets/titanic.txt
VARIABLE DESCRIPTIONS: Class (1 = first, 2 = second, 3 = third, 0 = crew) Age (1 = adult, 0 = child) Sex (1 = male, 0 = female) Survived (1 = yes, 0 = no)
n=2,201 observations (all people at risk)
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Sample Data File #2
Source: Frank Harrell and Thomas Cason, University of Virginia http://biostat.mc.vanderbilt.edu/twiki/pub/Main/DataSets/titanic.html
n=1,309 observations (passengers only) Note that age is numeric.
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Crosstabulation
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Mosaic Charts
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Mosaic Charts
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Mosaic Charts
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Mosaic Charts
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Multiple Correspondence Analysis
• Creates a map of the associations amongst the
categories of 2 or more variables.
• Seeks a small number of dimensions that
describe most of the variability or “inertia”
amongst the categories.
• Very useful in demonstrating the
interrelationships amongst the variables.
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Data Input
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Burt Table
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Multiple Mosaic Plot
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Inertia and Chi-Square Decomposition
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Scree Plot
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Correspondence Map
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Logistic Regression
• Binary logistic regression is designed to model situations in which there are only 2 possible outcomes, such as “survived” or “did not survive”.
• It estimates a model that predicts the probability of those outcomes as a function of 1 or more predictor variables.
• The predictor variables may be either quantitative or categorical.
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Bernoulli Events
• A Bernoulli event is an event in which 2
outcomes are possible.
• Let Yi = 1 if ith person survived, 0 otherwise.
• The pmf for a Bernoulli event is
𝑃𝑟𝑜𝑏 𝑦 = 𝑝𝑦(1 − 𝑝)1−𝑦 where 0 ≤ p ≤ 1
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Predictor Variables
• We now want to let p be a function of one or
more predictor variables X. In particular:
– X1 = class
– X2 = age
– X3 = sex
Then: 𝑝 = 𝑓(𝑋1, 𝑋2, 𝑋3)
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Logistic Model
• When modeling p, we need a model that remains between 0 and 1.
• Most common choice is the logistic model:
log𝑝
1 − 𝑝= 𝛽0 + 𝛽1𝑋1 + 𝛽2𝑋2 + ⋯
• It is a model for the log odds. If less than 0, odds are against the event. If greater than 0, odds are in favor of the event.
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Data Input
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Analysis Options
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Likelihood Ratio Test
• Full second order model
• Simplified model
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Plot of Fitted Model
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Predictions
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Recommended Reading
• Correspondence Analysis in Practice (second
edition) by Michael Greenacre (Chapman and
Hall, 2007)
• Applied Logistic Regression (third edition) by
David Hosmer and Stanley Lemeshow (Wiley,
2013)
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Recorded Webinar
• You may find the recorded webinar, PowerPoint
slides and sample data at:
www.statgraphics.com
• Look for “Instructional Videos”.