Developmental Models Lindon Eaves, Nathan Gillespie & Brad Verhulst Thu Mar 10, 2016 1:30pm – 3pm Mountain Time

Why run longitudinal models?

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Why run longitudinal models? Map changes in the magnitude of genetic & environmental influence across time ID enduring versus time dependent genetic or environmental risks Improve power to detect A, C & E

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Various models for analysing longitudinal data 1. Cholesky Decomposition 2. Latent growth curve model 3. Auto-regression model 4. Dual Change Score model

Models imply that you look at your variance-covariance matrix & have a theory about the nature of change

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Atheoretical longitudinal model 1. Cholesky Decomposition Advantages - logical: organized such that all factors are constrained to impact

later, but not earlier time points - requires few assumptions: can predict any pattern of change Disadvantages - atheoretical: no explicit hypothesis of change. Describes

patterns of change without accounting for them in terms of one or more simpler and, potentially more informative theoretical possibilities

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Theoretical longitudinal models After inspecting your observed variances-covariances in your repeated measures:

1. UNFOLDING Individual genetic and/or environmental differences in inherent growth patterns with age - Latent growth curve effects

2. ACCUMULATION of individual genetic and/or environmental

differences, which are more of less persistent - Autoregressive effects

3. Latent growth curve model + Auto-regression model (“Dual

Change Score model:”)

NB: INSPECT DATA

1. Latent growth curve model AKA ‘‘random regression’’, ‘‘hierarchial mixed’ or ‘‘latent growth curve” models” What does the LGC model predict? 1. Variation in latent true scores at each time point is a function of where you begin, or what you begin with, in terms of individual genetic and environmental differences….

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2. Variation in latent true scores at each time point is also a function of UNFOLDING individual genetic and environmental differences, over time, Unfolding may involve linear and non-linear rates of change.

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Latent growth modelling Developmental change = UNFOLDING of inherent, random genetic & environmental differences in the level & rates of change in behavior over time Model corresponds to special cases of the factor model in which factor loadings from the level (intercept) & change factors are functions of the coefficients of a priori contrasts on the levels of age at which the repeated measures were taken

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Latent growth modelling Recap – common pathway

Latent growth modeling Recap – common pathway

Latent growth modelling Add another latent factor fix the factor loadings

Latent growth modelling

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2. Auto-regression modelling AKA “simplex modelling” and “Sh%t-St%cks model” Example means

Example covariation matrix correlation matrix Cross-temporal correlations within subjects arise because time specific sources of individual differences are more or less persistent time, and may, ACCUMULATE during development. Giving rise to a developmental increase in genetic and/or environmental variance, and increased correlations between adjacent measures

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Auto-regression models

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Enables partitioning of variation at each time point into: - Transient genetic & environmental risks unique to each occasion - Persistent, enduring genetic & environmental risk factors Examples? - Snow-ball - Vocabulary acquisition - Emotional baggage

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Auto-regressive model examples

Dual Change Score model Latent growth curve model + Auto-regression model

Dual Change Score model

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Dual Change Score model Lisrel model (Jöreskog & Sörbom, 1996) to estimate expect covariance:

Λ x (I-Β)~ x (Γ x (ϕ) x Γ' + Ψ) x (I-Β)~' x Λ' + ϵ

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Pracatica Dual_change_score_model.R

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2.040.82 -0.20