a**a
发帖数: 8 | 1 Hi need some help from your guys:
I have a data set which include variables Y and X.
Each of these two variables have measurements for
100 patients and at 10 time points. We want to build
a model which can Y(t+1) based on X(t), t=1,2,...,10.
The data structure is like:
Data for Y: row is patients (70) and column is time points (10)
y11, y12,..., y110
y21, y22,.., y210
...
y701, y702,...,y7010
Data for X: row is patients (70) and column is time points (10)
x11, x12,..., x110
x21, x22,.., x210
. | j*****e
发帖数: 182 | 2 This is not a time series data, since you have 100 patients, not one patient
. It is a repeated measurement data with time dependent covariates(???).
Check some experimental design book on mixed models. | s**********e
发帖数: 46 | 3 This IS a problem of time series analysis although you only have 10 time
points. If you want the relations of X(t+1) or Y(t+1) with X(t) or Y(t), you
can try multivariate autoregressive model (AR(1)). By fitting a vector AR(1
), one thing you have to be careful is that your data is including two time
series (10 points) with multiple realizations (70 patients).
Another thing you may have to keep in mind is that AR model assumes
stationary process. You may have to check your data if it is close to
【在 a**a 的大作中提到】
: Hi need some help from your guys:
: I have a data set which include variables Y and X.
: Each of these two variables have measurements for
: 100 patients and at 10 time points. We want to build
: a model which can Y(t+1) based on X(t), t=1,2,...,10.
: The data structure is like:
: Data for Y: row is patients (70) and column is time points (10)
: y11, y12,..., y110
: y21, y22,.., y210
: ...
| a**a
发帖数: 8 | 4 Thanks for both of your's comments!
Hi, snowwhitebee
To use multivariate autoregressive model (AR(1)), my major problem is that I
do not know how to set the 70 realizations in the model. For the standard
multivariate autoregressive model, say there are two variables x, y and
there are 10 time measurements for the two variables, then the model will
like:
y(t)=c1 + pi1 * y(t-1) + pi2 * x(t-1) + e1(t)
x(t)=c2 + pi3 * x(t-1) + pi4 * y(t-1) + e2(t)
Although what I really want is use x(t-1) to predict | s**********e
发帖数: 46 | 5 Yule-Walker equations are generally used to estimate the parameters in a AR
model.That is you have to compute the covariance matrix first. The
difference of computing covariance matrix for short time series with
multiple realizations instead of for long time series is that you can only
get the covariance matrix at up to lag 9 since you only have 10 points. You
can compute the covariance matrices for each short series, then average
across the realizations (70 patients). But I expect a poor fitti | j*****e
发帖数: 182 | 6 I said this is not a time series data because you can not use traditional
time series methods to analyze it. Sure, for each patient, you have a short
series. But traditional method is developed for long series. Forcing those
models on such a short series will lead to unstable models.
Also, average whatever you got is not a good solution, since how are you
going to report the SE of your estimate? There is an across-patient
variability, and within-patient variability.
Using linear mixed model, yo | h******a
发帖数: 198 | 7 这是longitudinal data，与一般的time series的区别是，时间点较少，但是有多个个体
可以用random coefficient regression 解决
如果你想要更复杂的模型，可以考虑 Growth Mixture Model, 可以解决heterogeneous
的情况。Growth Mixture Model认为这70个人是来自 几个group， group number 未知但是固定。我用过一个SAS 的软件包， PROC TRAJ 可以做Growth Mixture Model 你可以试一试 | l********3
发帖数: 69 | 8 在google搜 applied longtitudinal analysis
有类似的例子，还有相关数据。
可以具体看一下这本书的chap 6,7,8 | a**a
发帖数: 8 | 9 Thanks all!
let me repeat the data structure again:
The data structure is like:
Data for Y: row is patients (70) and column is time points (10)
y11, y12,..., y110
y21, y22,.., y210
...
y701, y702,...,y7010
Data for X: row is patients (70) and column is time points (10)
x11, x12,..., x110
x21, x22,.., x210
...
x701, x702,...,x7010
Our objective is forecasting, that is, we want to build a model like y(t)
can be predicted by x(t+1), t=1,2,...,10. like y(1) can be predicted by x(2)
, y(2) can be pre | j*****e
发帖数: 182 | 10 I don't use R. A good book on how to use SAS analyzing repeated measurement
is the SAS mixed model book published in 2006. Another starter book is
Miliken and Johnson's book on messy data.
In biometrics, data with repeated measurement is called longitudinal data.
You may also find reference book on the analysis of longitudinal data.
For your problem, the covariate is time-dependent. It might be hard to find
a direct solution out of a text book. Search on CIS for some articles in
this area.
Also, | h******a
发帖数: 198 | |
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