Index A Bayesian sampling, 392 Acceleration, 199 Behavioral dynamics, 218 Adjacency matrix, 115 Bergstrom’s statistic, 345 AIC, 212 Between-and within-person changes, 259 Akaike information criterion, 208 BFGS secant updates, 402 Aliasing, 11 Bias, 107 Aliasing problem, 329 BIC, 212 Ambulatory assessment, 245 Bifurcation, 390 Amplitude, 293 Boundaries, 225 Approximate discrete model, 11 Boundary effect or edge effect, 255–256 ARMAX model, 2 Bowman-Shenton test, 314 Assumption of invertibility, 325 Box-Ljung statistic, 314 Attractor force, 67 Box-Pierce test, 153 Attribute evolution, 117–118 BPS, 67–68 Augmented state space form, 328 Brownian bridge, 412 Autocorrelation, 29 Brownian motion, 59 Auto-covariance function, 372 Business cycle fluctuations, 283 Autoeffects, 38, 184 Business cycle theory, 290 Autoregression, 180 Autoregression coefficients, 169 Autoregressive and moving average (ARMA) C model, 2 CARIMA, 346 CARMA, 1 Causal inference, 106 B Chaotic Lorenz model, 389 Backward operator, 405 Chronometric factor models, 266 Backward pass, 310 Classification and regression tree (CART), 264 Base and input processes, 102 Closed-form solution, 319 Base process, 88 Coevolution model, 120 Bayes factor, 74 Coevolution of networks and behaviors, 112 Bayes formula, 392 COGITO study, 273 Bayesian estimation, 56 Coherence, 370 Bayesian framework, 55–76 Cointegration, 325 Bayesian inference, 68 Competitive equilibrium, 285 Bayesian information criterion, 208 Complete mediation, 197–198 © Springer International Publishing AG, part of Springer Nature 2018 437 K. van Montfort et al. (eds.), Continuous Time Modeling in the Behavioral and Related Sciences, https://doi.org/10.1007/978-3-319-77219-6 438 Index Complex, 46–48 Distributed lag structures, 284 Conditional distribution of OU process Drift function, 397–398 positions, 62 Drift matrix, 31 Conditional expectation, 361 dse, 146 Conditional variances, 361 DT-VAR model, 32 Confounded, 92 Dummy variable, 15 Constraints, 145 Dyadic covariates, 117 Continuous-discrete extended Kalman filter Dyadic interactions, 135–160 (CDEKF), 210 DynAffect, 58 Continuous-discrete state-space models, Dynamic equilibrium models, 283 389–430 dynr, 208 Continuum limit, 424–430 Convolution, 256 Convolution filtering, 242 E Core affect, 58 Ecological momentary assessment (EMA), 57, Covariates, 75 245 Cross-effects, 38, 184 Eigenvalue decomposition, 341 Cross-lagged effects, 46 Eigenvalues, 33, 46–48, 330 Cross-lagged panel model (CLPM), 180, 192 Embedding, 11 Cross-regression coefficient, 169 Embedding dimension, 241 Cross-spectrum, 369 Endogenous variables, 166 ctarmaRcpp, 360 Ensemble technique, 278 Ctsem, 3 Entropy, 262 CTSMr, 146 Environmental Kuznets curve (EKC), 294 Cycle, 224 Equally spaced measurements, 57 Cyclical behaviour, 330 Equidistant, 115 Equilibrium, 31 Ergodicity, 337 D Error cancelation, 254 Damped linear oscillator model, 213 Error correction Model (ECM), 334 Damped oscillation, 92 ETK, 404 Damped oscillator model, 208 Euler approximation, 338 Damping parameter, 213 Euler density, 392, 395 Damping stage, 223 Euler equation, 291 Decay parameter, 250 Euler-Maruyama approximation, 394, 411 Decision trees, 260 Euler’s number, 142 Definition variables, 268 Euler transition kernel, 403–404 Delays, 284 Exact discrete model (EDM), 1 Delta function, 406, 426 Exact discrete time model, 318 Delta method, 122 Exact discrete time representation, 317–351 Deterministic, 184 Experience sampling, 245 Deterministic drift function, 215 Exponentially weighted moving average Differential operator, 365 (EWMA), 308 DIFFUSION, 96 Exponential trend, 85 Diffusion matrix, 31 Extended Kalman filter (EKF), 211 Diffusion-type models, 319 Extended Kalman sampling (EKS), 409 Dirac delta, 105 Extended/unscented Kalman smoother, 411 Dirac delta function, 82 Extrapolating, 45 Direct effect, 180 Discretisation bias, 338 Disequilibrium models, 319 F Dissipation, 91–92 Factor loadings, 84 Distributed approximating functional (DAF), Feasibility constraint, 290 406 Filtered, 310 Index 439 Filtering, 210 Inertia, 30 Finite differences, 405 Initial conditions (ICs), 209 First-order, 28 Input processes, 88, 93 First-order conditions, 290 Inputs, 80 Fisher information matrix, 148 Instantaneous change, 137 Flow variables, 319 Integration, 82 Fokker-Planck equation, 392 Intensive longitudinal data (ILD), 27–51, 57, Forward and reverse smoothing, 234 259 Forward pass, 310 Interindividual, 68 Fourier transforms, 360, 368 Interpolation spline method, 248 Full information maximum likelihood (FIML) Interpolation splines with resampling, 240 estimation, 165 Interventions, 79–108 Functional derivatives, 420 Intraindividual, 68 Intraindividual variability, 213 Inverted U-shaped, 296 G Ipsative, 253 Gauss-Hermite filter (GHF), 415 Irregularly spaced measurement, 131 Gauss-Hermite integration, 401 Irregularly spaced observations, 208 Gaussian, 214 Itô integral, 142 Gaussian likelihood function, 335 Itô’s lemma, 404 Gelman-Rubin Rˆ statistic, 70 Generalized inverse, 395 Geometrical brownian motion (GBM), J 406–410 Jaccard index, 115 German Socio-Economic Panel (GSOEP), 164 Jackknife methods, 338 Ginzburg-Landau model, 390 Jacobian matrix, 211 Granger causality, 330–332 Jacobians, 412 Growth and business cycle theory, 283–302 Growth curve models, 199 K Gumbel distribution, 119 Kalman filter, 3, 16 Kalman gain, 140 Kalman importance sampling, 389–430 H Kalman smoother, 16 Hamiltonian matrix, 329 Kernel matrix, 398 Hessian matrix, 149, 226 Kronecker product, 83 Heterogeneity, 260 Kullback-Leibler divergence, 265 Heun method, 398 Hierarchical Bayesian approach, 81 Higher-order systems, 323 L Highest density interval (HDI), 74 Lagged and instantaneous effects dilemma, Home base, 215 170 Homeostatic value, 199 Lagged residuals, 153 Homophily, 129 Lagrangian, 397 Langevin equation, 59 Langevin sampler, 392, 420–424 I Latent differential equation (LDE) models, 240 Identifiability, 231 Latent growth curve model (LGCM), 265 Identification, 328 Latent state variables, 216 Importance sampling, 396 Law of permanent inventory, 286 Impulse effect, 85–87 Level change, 90 Impulse response, 40 Level change effect, 87–90 Impulse response functions (IRFs), 39 Likelihood, 131 Increments, 393 Likelihood function, 69 Indirect effect, 180 Likelihood ratio test, 191 440 Index Linear stochastic differential equations Network-attribute panel data, 112 (LSDE), 146 Network autocorrelation, 114 Ljung-Box test, 153 Network boundary problem, 112 LLTK, 404 Network density, 124 Local indeterminacy, 284 Network evolution model, 118 Local level, 307–309 Network outdegree, 131 Local linear approximation (LLA), 3 Network structure, 111–132 Local linearization (LL) method, 395 Neutrally stable, 48 Local linear trend models, 307–309 Newton algorithm, 402 Logarithmic transformations, 272 Newton-Raphson method, 122 Logistic growth, 220 Non-convergence, 226 Log-likelihood function, 225 Nonlinear, 32 Lower triangular matrix, 82 Nonlinear continuous-discrete state-space LSDE package, 146 model, 393 Nonparametrically, 334 Nonpositive-definite, 226 M Nonsingular, 324 Manifest intercepts, 84 Nonstationarity, 319, 332–335 MANIFESTTRAITVAR, 86 Nullclines, 43 Markov chain model, 165 Numerical integration, 395 Markov process, 400 Nyquist frequency, 383 Matrix differentiation, 158 Nyquist limit, 242 Matrix exponential, 10, 50 Matrix square root, 209 McDonald-Swaminathan rules, 158 O mctarmaRcpp, 360 Observation or measurement equation, 307 Mean-reverting process, 60 Onsager-Machlup functional, 397 Measurement error, 2 OpenMx, 146, 268 Measurement noise, 209 Optimal control, 284 Mediation, 179–202 Optimal control theory, 300 Mediators, 89 Ordinary differential equation (ODE) model, Meta-analysis, 132 209 Metropolis-Hastings algorithm, 392 Ornstein-Uhlenbeck model, 31, 56, 58 Missing-at-random (MAR) assumption, 165 Oscillating movements, 11 Missing data, 171 Oscillation, 85 Missing responses, 116 Oversampling, 15 Mixed frequency data, 336 Overshooting, 296 Mixed sample case, 325 Ozaki scheme, 398 Mixture modeling, 260 Models, 28 Model selection, 279 P Monte Carlo methods, 56 Padé, 341 Monte Carlo simulations, 242 Panel data, 136 Moving average disturbance, 325 Pareto optimal, 294 Multilevel datasets, 46 Partial adjustment equations, 349 Multilevel/hierarchical, 65–68 Partial adjustment processes, 319 Multinomial, 56 Partial differential equation, 392 Multiple unit roots, 330 Path diagram, 138 Multi-time scale processes, 206–208 Pendulums, 56 Multivariate normal, 82 Period-specific parameter, 118 Persistent level change, 88 N Person-specific intervals, 268 Necessary, 329 Phase function, 370 Neoclassical production function, 285 Phase space, 396 Index 441 Piecewise continuous, 300 S Planned missingness, 240, 247 Saddle, 292 Policy function, 292 Saddle point, 48 Polygonal approximation, 15 Sampling frequencies, 319 Portmanteau tests, 153 Sampling interval, 331 Posterior distribution, 69 Sampling interval misspecification, 239–257 Posteriori density (measurement update), 391 SAS-CALIS, 166 Predetermined, 296 Schwarz Bayesian model selection criterion Predicted, 310 (SBC), 345 Prediction error decomposition (PED), 140, Score function, 401–402 215 SDEs, 143–144 Prediction errors, 211 Selection matrix, 307 Predictive accuracy, 279 Self-organization, 206 Predictor, 82 SEM trees, 264 Prior bounds, 330 Set point parameter, 213 Prior distribution, 69 Slope loadings, 268 Priori density (time update), Smoothed state, 310 391 Smoothing, 212 Priori restrictions, 331 Social planner, 290 Process error, 250 Solow growth model,