Hi,

I am using ns() to model the effect of time on some outcome y
[ specifically, I am using polr() in a model of the form

mod1=polr(y~x1+x2*ns(Year,df=3),...)  , with x1 and x2 denoting several
covariates each ]


I understand how to use the spline basis as recorded in the model matrix in
order to reproduce the model fit and to generate curves of the point
estimates of the time effect, including its interactions with other
covariates.

My question is about confidence bands. So far, I tried to calculate these in
a straightforward manner using the coefficients' estimated covariance
matrix. [ e.g., Var (a+b) = Var(a) + Var(b) + 2Cov(a,b) ]

Common sense suggests that the bands will be narrowest in the middle of the
time period studied and widening towards the edges. However, the model fit
seems to default to zero time-effect errors at the start of the period,
gradually widening as time progresses - which is not supported by the data
(in my case the data are almost evenly distributed across time by design).

In my application the time effect is of major importance and not a nuisance
variable, so it is crucial for me to get this right.

I tried to add an intercept to the ns() function, but this appears to
interfere with the model's intercept estimate and generates errors.

Any suggestions welcome...

Thanks in advance,
Assaf Oron

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