CODEWITHSUNDEEP
rsimulationspatstat
Jingming
Jingming

Reputation: 11

confidence interval of estimates in a fitted hybrid model by spatstat

hybrid Gibbs models are flexible for fitting spatial pattern data, however, I am confused on how to get the confidence interval for the fitted model's estimate. for instance, I fitted a hybrid geyer model including a hardcore and a geyer saturation components, got the estimates:

Mo.hybrid<-Hybrid(H=Hardcore(), G=Geyer(81,1))
my.hybrid<-ppm(my.X~1,Mo.hybrid, correction="bord")
#beta = 1.629279e-06
#Hard core distance:    31.85573
#Fitted G interaction parameter gamma:   10.241487

what I interested is the gamma, which present the aggregation of points. obviously, the data X is a sample, i.e., of cells in a anatomical image. in order to report statistical result, a confidence interval for gamma is needed. however, i do not have replicates for the image data. can i simlate 10 time of the fitted hybrid model, then refitted them to get confidence interval of the estimate? something like:

mo.Y<-rmhmodel(cif=c("hardcore","geyer"), 
           par=list(list(beta=1.629279e-06,hc=31.85573),
                    list(beta=1, gamma=10.241487,r=81,sat=1)), w=my.X)
Y1<-rmh(model=mo.Y, control = list(nrep=1e6,p=1, fixall=TRUE), 
start=list(n.start=c(npoint(my.X))))
Y1.fit<-ppm(Y1~1, Mo.hybrid,rbord=0.1)
# simulate and fit Y2,Y3,...Y10 in same way

or:

Y10<-simulate(my.hybrid,nsim=10)
Y1.fit<-ppm(Y10[1]~1, Mo.hybrid,rbord=0.1)
# fit Y2,Y3,...Y10 in same way

certainly, the algorithms is different, the rmh() can control simulated intensity while the simulate() does not. now the questions are: is it right to use simualtion to get confidence interval of estimate? or the fitted model can provide estimate interval that could be extracted? if simulation is ok, which algorithm is better in my case?

Upvotes: 0

Views: 99

Answers (1)

Adrian Baddeley
Adrian Baddeley

Reputation: 2973

The function confint calculates confidence intervals for the canonical parameters of a statistical model. It is defined in the standard stats package. You can apply it to fitted point process models in spatstat: in your example just type confint(my.hybrid).

You wanted a confidence interval for the non-canonical parameter gamma. The canonical parameter is theta = log(gamma) so if you do exp(confint(my.hybrid) you can read off the confidence interval for gamma.

Confidence intervals and other forms of inference for fitted point process models are discussed in detail in the spatstat book chapters 9, 10 and 13.

The confidence intervals described above are the asymptotic ones (based on the asymptotic variance matrix using the central limit theorem).

If you really wanted to estimate the variance-covariance matrix by simulation, it would be safer and easier to fit the model using method='ho' (which performs the simulation) and then apply confint as before (which would then use the variance of the simulations rather than the asymptotic variance).

rmh.ppm and simulate.ppm are essentially the same algorithm, apart from some book-keeping. The differences observed in your example occur because you passed different arguments. You could have passed the same arguments to either of these functions.

Upvotes: 1

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