Mplus Users Guide v6.. - Muthén & Muthén

CHAPTER 17ATThe AT option is used with TYPE=RANDOM to define a growth modelwith individually-varying times of observation for the outcome variable.AT is short for measured at. It is used in conjunction with the | symbolto name and define the random effect variables in a growth model whichare referred to as growth factors.Four types of growth models can be defined using AT and the | symbol:an intercept only model, a model with two growth factors, a model withthree growth factors, and a model with four growth factors. The namesof the random effect variables are specified on the left-hand side of the |symbol. The number of names determines which of the four modelsmodel will be estimated. One name is needed for an intercept onlymodel and it refers to the intercept growth factor. Two names areneeded for a model with two growth factors: the first one is for theintercept growth factor and the second one is for the slope growth factorthat uses the time scores to the power of one. Three names are neededfor a model with three growth factors: the first one is for the interceptgrowth factor; the second one is for the slope growth factor that uses thetime scores to the power of one; and the third one is for the slope growthfactor that uses the time scores to the power of two. Four names areneeded for a model with four growth factors: the first one is for theintercept growth factor; the second one is for the slope growth factor thatuses the time scores to the power of one; the third one is for the slopegrowth factor that uses the time scores to the power of two; and thefourth one is for the slope growth factor that uses the time scores to thepower of three. Following are examples of how to specify these growthmodels:intercpt | y1 y2 y3 y4 AT t1 t2 t3 t4;intercpt slope1 | y1 y2 y3 y4 AT t1 t2 t3 t4;intercpt slope1 slope2 | y1 y2 y3 y4 AT t1 t2 t3 t4;intercpt slope1 slope2 slope3 | y1 y2 y3 y4 AT t1 t2 t3 t4;where intercpt, slope1, slope2, and slope3 are the names of the interceptand slope growth factors; y1, y2, y3, and y4 are the outcome variables inthe growth model; and t1, t2, t3, and t4 are observed variables in the dataset that contain information on times of measurement. The TSCORESoption of the VARIABLE command is used to identify the variables thatcontain information about individually-varying times of observation for610