Slide 1 - 7 October 2014

• Modeling
• MODELING GROWTH: FROM DINOSAURS TO CHILDREN

Slide 3 - To better understand their biology, metabolism, and behavior

• Why Model Dinosaur Growth?

Slide 4 - 4

• Commonalities with modeling child growth
• The importance of best practices, especially when data is imperfect
• Choosing appropriate variables
• Choosing the mathematical model that objectively works best
• Fitting curves appropriately
• Understanding and respecting the limitations of data and models

Slide 6 - 6

• Lines of arrested growth (LAGS)
• Velociraptor
• Tenontosaurus

Slide 8 - 8

• Estimating age and size from fossilized bone
• Lines of arrested growth (LAGs)
• Estimate age from LAG count
• Estimate mass from circumference of major bones:
• M = a (cfemur + chumerus)b
• for quadrupeds,
• a = 0.078, b = 2.73
• for bipeds,
• a = 0.16, b =2.73

Slide 10 - Analyzed 31 Sets of Dinosaur Growth Data, Spanning 14 Taxa

Slide 12 - When complete data is not available on individuals, aggregating data can enable reconstruction of plausible growth trajectories

• Some researchers do the fitting by eye
• Least-squares optimization is replicable and more accurate
• Need to use non-integer scaling factors (not every individual has the same birthday!)
• 12
• Constructing longitudinal seriesfrom sparse data

Slide 14 - Testing Fits to Multiple Models

• 14
• 21 increasing functions
• 14 asymptotic attenuating
• 49 asymptotic sigmoidal
• 84 functions × 31 data sets = 2,604 fits
• parameters
• functions
• 1
• 4
• 2
• 21
• 3
• 31
• 4
• 28
• Using more free parameters may improve the fit, but not always enough to justify the additional degrees of freedom

Slide 16 - 16

• Growth IS USUALLY (BUT NOT ALWAYS) heteroscedastic
• Wandering albatross
• Heteroscedastic growth: the distribution of body sizes widens substantially with age as individual growth trajectories diverge
• At age 50d, σ = 1,115; at age 250d, σ = 1,505

Slide 18 - Increases the likelihood that an algorithm will find the best fit, and decreases the probability of algorithm failure

• Tested using synthetic data set and six commonly used global fitting algorithms from R and Mathematica
• A New Preprocessing transformation for Fitting Models

Slide 19 - 19

• From bone circumference and age estimates, we calculated the likely peak growth rate
• Example: Tyrannosaurus
• Maximum bone growth rate occurs at age 2
• Bone circumference (cm)
• Age (y)
• Peak mass growth rate: 365 kg/yr
• PER YEAR

Slide 21 - Almost all previous analyses in the literature were affected by one or more methodological issues

• 21
• Irreproducible fits
• Use of subjective, rather than objective, criteria to select among models
• Inappropriate choice of independent variable
• Incorrect or hand-tweaked data and curve-fitting
• Attempted replications of prior published results
• Age
• Mass

Slide 23 - 23

• Choose the right independent variable
• Linear regression methods assume it has no error
• Monte Carlo analysis illustrates the consequence of choosing wrong: a different mean and a much greater standard deviation
• Lessons Applicable to Modeling ChilD Growth
• Age as the independent variable
• Time as the independent variable

Slide 24 - 24

• Choose the right independent variable
• Linear regression methods assume it has no error
• Monte Carlo analysis illustrates the consequence of choosing wrong: a different mean and a much greater standard deviation
• Lessons Applicable to Modeling ChilD Growth
• Age as the independent variable
• Time as the independent variable

Slide 26 - 26

• Try multiple alternative models
• Don’t overfit by using too many parameters
• Respect model constraints
• Use an objective criterion, such as AICc, to select the best model
• All goodness-of-fit metrics are local to the data points—there is no legitimate prediction beyond the limits of the data
• Lessons Applicable to Modeling Child Growth

Slide 28 - 28

• If the shoe fits—it doesn’t necessarily mean anything
• Every growth model has a linear phase!
• Lessons Applicable to Modeling Child Growth

Slide 30 - 30

• Avoid unjustified extrapolation by estimating error and plotting confidence intervals
• Outside the bounds of the data, CIs grow wide quickly
• Lessons Applicable to Modeling Child Growth

Slide 32 - Cross-sectional data sets cannot accurately simulate longitudinal series

• Longitudinal vs. Cross-sectional data
• Standard curve-fitting algorithms assume uncorrelated errors
• This assumption is violated by longitudinal data sets that follow individuals over time

Slide 34 - Cross-sectional data sets cannot accurately simulate longitudinal series

• Longitudinal vs. Cross-sectional data
• Source data: longitudinal growth measurements on 100 flamingos
• 100 longitudinal fits: fit the same function to each individual series
• 100 cross-sectional fits: fit the same function as above to data sets of randomly selected points representing the
• entire life span
• Values of coefficient a b c

Slide 36 - Following individuals for many years enables insights into the effects of path history

• Need to use models and measures designed for longitudinal series
• The Power of Longitudinal Data

Slide 38 - 38

• Weighted Least Squares Analysis

Slide 39 - Improper measurement of the independent variable attenuates relationships.

• Jerry Hausman, M.I.T., in Journal of Economic Perspectives 15:4 (2001)
• 39
• The Iron Law of econometrics
• Nigeria: +89%
• Oshodi BA. Energy Economics and Project Financing Options in Nigeria. Rochester, NY: Social Science Research Network, 2014
• Zambia: +24%
• Jerven M. Poor Numbers: How We Are Misled by African Development Statistics and What to Do about It. Ithaca, NY: Cornell University Press, 2013.
• Ghana: +63%
• Jerven M, Duncan ME. Revising GDP estimates in sub-Saharan Africa: lessons from Ghana. Afr Stat J 2012; 15: 13–24.
• GDP measurements are noisy and often inaccurate even in developed economies
• Changes to national accounting systems can cause large artificial changes

Slide 41 - Consensus view: Stunting Falls as GDP Rises

• Absolute decline in prevalence
• Relative decline (% of previous prevalence)

Slide 43 - Underweight Also goes down when GDP goes up

• Absolute decline in prevalence
• Relative decline (% of previous prevalence)

Slide 44

• Countries where GDP per capita was growing were 67% more likely to reduce the prevalence of child stunting

Slide 46

• Causal or Simply Correlated?
• Stunting and sanitation

Slide 48

• Causal or Simply Correlated?
• Stunting and maternal education