Hi,

I am using a two part hurdle model to account for zero inflation and
overdispersion in my count data. I would like to account for a segmented or
breakpoint relationship in the binomial logistic hurdle model and pass
these results onto the count model (negative binomial).

Using the segemented package I have determined that my data supports one
breakpoint at 3.85. The slope to this point is significant and will affect
the presence of zeros in a linear fashion. The slope > 3.85 is
non-significant and estimated to not help predict the presence of zeros in
the data (threshold effect). Here are the results from this model

Estimated Break-Point(s):
   Est. St.Err
 3.853  1.372

t value for the gap-variable(s) V:  0

Meaningful coefficients of the linear terms:
               Estimate Std. Error z value Pr(>|z|)
(Intercept)     -0.2750     0.3556  -0.774   0.4392
approach_km     -0.4520     0.2184  -2.069   0.0385 *
sea2             0.3627     0.2280   1.591   0.1117
U1.approach_km   0.4543     0.2188   2.076       NA

U1.approach_km is the estimate for the second slope. The actual estimated
slope for the section section is the difference between this value and the
approach_km value (0.0023).

I think that I have found a way to "maually" code this into the hurdle
model as follows

hurdle.fit <- hurdle(tot_f ~  x1 + x2 + x3 | approach_km +
I(pmax(approach_km-3.849,0)) + sea )

When I look at the estimated coefficients from the "manual" code it gives
the same values. However, the std.errors are estimated lower.

Zero hurdle model coefficients (binomial with logit link):
                                Estimate Std. Error z value Pr(>|z|)
(Intercept)                     -0.27441    0.29347  -0.935    0.350
approach_km                     -0.45261    0.09993  -4.529 5.92e-06 ***
I(pmax(approach_km - 3.849, 0))  0.45486    0.10723   4.242 2.22e-05 ***
sea2                             0.36271    0.22803   1.591    0.112

Question # 1: Does the hurdle equation use the standard errors from the
zero model when building the count predictions? If no then I guess I would
not have to worry about this and can just report the original std.errors
and associated p values from the segemented object in the pub.
Question # 2: If the count model uses the std.errors, how can I reformulate
this equation to generate the original std.errors.

Thanks, Tim

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