# 繼續 (1)，這裏主要是上的課程的筆記
# YouTube: Crurran-Bauer Analytics
1. linear regression: multiple regression
https://www.youtube.com/watch?v=Qyw2_3cVpa0&list=PLQGe6zcSJT0V4xC1NDyQePkyxUj8LWLnD&index=5
- with formula
- with algebra
2. SEM
https://www.youtube.com/watch?v=QkXTdTCF3PI&list=PLQGe6zcSJT0XCCmKAxqiA8AGl-z6HYn5B&index=2
(1) introduction
(2) path analysis
~ what are those shapes and arrows mean: regression, predictors, latent variables, residuals, correlations, association
~ what are differences between normal models and structural models: mediators...and others, dependent variables, structured relations
~ how to design the path diagrams: can be hypothesis-driven, then test them; or data-driven (could be dangerous)
~ test the indirect effect (with one or more mediators): should be tested all of them as a unit (@ 19:45)
(3) factor analysis
~ observed factors/data
~ latent factors
(4) SEM
- model fit
~ the residuals
~ observed data and the model
~ several indices to evaluate the model
he describes relative goodness-of-fit indices (TLI, CFI, IFI) and absolute goodness-of-fit indices (RMSEA) as well as the standardized root mean residual (SRMR). He concludes with recommendations for how all of these measures of model fit can be used in practice.
~ REF:
Bollen, K. A., & Long, J. S. (1992). Tests for structural equation models: introduction. Sociological Methods & Research, 21, 123-131.
Browne, M. W., & Cudeck, R. (1992). Alternative ways of assessing model fit. Sociological Methods & Research, 21, 230-258.
Chen, F., Curran, P. J., Bollen, K. A., Kirby, J., & Paxton, P. (2008). An empirical evaluation of the use of fixed cutoff points in RMSEA test statistic in structural equation models. Sociological Methods & Research, 36, 462-494.
Saris, W. E., Satorra, A., & van der Veld, W. M. (2009). Testing structural equation models or detection of misspecifications? Structural Equation Modeling, 16, 561- 582.
West, S. G., Taylor, A. B., & Wu, W. (2012). Model fit and model selection in structural equation modeling. Handbook of structural equation modeling, 209-231.
(5) advanced topics
different datasets
3. growth curve modeling
https://www.youtube.com/watch?v=2hV7MyEX2UA&list=PLQGe6zcSJT0VxMZUN6DBuhIoCRZNoA2Vz
(1) what is growth curve modeling?
~ intra-subject: starting point, slope
~ inter-subjet
~ time variant and invariant
(2) the coding of time
~ can be different allocation, from the beginning, middle or backwards
~ REF
Biesanz, J.C., Deeb-Sossa, N., Aubrecht, A.M., Bollen, K.A., & Curran, P.J. (2004). The role of coding time in estimating and interpreting growth curve models. Psychological Methods, 9, 30-52.
Hancock, G. R., & Choi, J. (2006). A vernacular for linear latent growth models. Structural Equation Modeling, 13, 352-377
(3) multilevel modeling framework
~ allow nested structure with repeated measurements
~ level1, level 2, while level2 is nested for level 1
~ level 1 can be each kid, level 2 can be the repeated measurement like 3 assessments that each kid took
~ level 1, within subject, intra individual differences; level 2, bewteen subjects, inter-individual differences
~ the principle is, in MLM, you can also model the individual differences into the model, as a level
~ unconditional means on predictors, conditional means we have predictors, like gender; these can be on level 2
~ time variant and time invariant @17:50, can be on both level 1 and level 2, can be interacted within level, or cross level
~ what if we level 3? 20:00, level 1 can be age, level 2 can be child, level 3 can be classroom effect
(4) an SEM framework
(5) nonlinear trajectories
~ linear: the changes between each time point are equal, like all 0.5...
~ nonlinear: the changes are inequal, like reading ability
~ linear slope, and the covariant between different changes
~ quadratic change: linear slope and the factor loading
~ cubic: ?
~ (free loading model vs. fixed model)
~ * three approaches can be used in nonlinear trajectories:
the family of polynomials quadratic cubic quartic model (can do either in SEM or MLM)
piecewise linear (piece = factor) (can do either in SEM or MLM)
free learning model or latent basis function: get the optimal fit (only in SEM)
# more like structural latent curve model
~ REF
Flora, D. B. (2008). Specifying piecewise latent trajectory models for longitudinal data. Structural Equation Modeling, 15, 513-533.
Grimm, K. J., & Ram, N. (2009). Nonlinear growth models in Mplus and SAS. Structural Equation Modeling, 16, 676-701.
(6) Time-invariant covariates
~ Once an optimal model of linear or nonlinear change has been established, it is often of interest to then incorporate one or more time-invariant covariates (TICs) as predictors of the growth factors.
~ TICs are predictors that do not change as a function of time... Examples of TICs include biological sex, country of origin, birth order, or any person-level characteristic assessed only at the initial time point.
~ TICs are used as predictors of the latent growth factors in the SEM or entered as Level 2 predictors in the MLM; in both approaches, tests are obtained regarding the extent to which information on the TIC in part contributes to the growth process under study.
~ Although the interpretation of predictors of the intercept factor are straightforward, predictors of the slope factor are more complex given the interaction between the predictor and time.
~ These slope effects must be probed further to more fully understand the nature of the effect. Patrick discusses these issues in greater details and makes recommendations for using these in practice.
~ REF
Bauer, D.J., & Curran, P.J. (2005). Probing interactions in fixed and multilevel regression: Inferential and graphical techniques. Multivariate Behavioral Research, 40, 373-400.
Curran, P. J., Bauer, D. J., & Willoughby, M. T. (2004). Testing main effects and interactions in latent curve analysis. Psychological Methods, 9, 220-237.
Preacher, K. J., Curran, P. J., & Bauer, D. J. (2006). Computational tools for probing interactions in multiple linear regression, multilevel modeling, and latent curve analysis. Journal of Educational and Behavioral Statistics, 31, 437-448.
(7) Time-varying covariates
~ the inclusion of time-varying covariates (TVCs), predictors with numerical values that can differ across time.
~ Examples of TVCs are numerous and include time-specific measures of depression, anxiety, substance use, marital status, onset of diagnosis, or dropout from treatment, among many others.
~ When TICs are included in a growth model, the time-invariant predictors are used to directly predict the growth factors (e.g., intercept, slope). In contrast, when TVCs are included in a growth model, the effects of the time-varying predictors bypass the growth factors and directly influence the repeated measures.
~ There are many ways that TVC influences can be included in the model, and models can be further extended to include both TICs and TVCs simultaneously.
~ the time variance should be modeled in a growth model, cuz itself is changing; although it is changing with the whole growth process
(8) multivariate growth
~ conditional and unconditional
~ univariate, bivariate, multivariate
~ several model, like ALT
~ latent curve model: interestingly, we can use the changes between time1 and time2 to predict the changes between time 2 and time 3
~ REF
Bollen, K.A., & Curran, P.J. (2004). Autoregressive latent trajectory (ALT) models: A synthesis of two traditions. Sociological Methods and Research, 32, 336-383.
Curran, P.J., Howard, A.L., Bainter, S.A., Lane, S.T., & McGinley J.S. (2013). The separation of between-person and within-person components of individual change over time: A latent curve model with structured residuals. Journal of Consulting and Clinical Psychology, 82, 879-894.
Grimm, K. J., An, Y., McArdle, J. J., Zonderman, A. B., & Resnick, S. M. (2012). Recent changes leading to subsequent changes: Extensions of multivariate latent difference score models. Structural equation modeling: a multidisciplinary journal, 19, 268-292.
Grimm, K. J., Ram, N., & Estabrook, R. (2017). Growth modeling: Structural equation and multilevel modeling approaches. New York, NY: Guilford.
(9) how to choose between SEM and MLM, how can we design which model to use, what characteristics they have...
~ MLM: nested data, as repeated measurement (long format)
~ SEM: the repeated measurements as observed indicators, then become underlying as latent factors, which can be later on as growth trajectory analysis (wide format), can test the mediating factors