Re: Maximum likelihood estimator and multiple maxima


>> Are the predicted values also virtually identical at these different parameter
>> points? If so, some of the model parameters may not be identifiable.

>The predicted value is a function, m(z) say, where for the current data set
>(157 points) z takes values within the interval (0,1.8).

Unfortunately, this is the only part of your reply that I understand.
Maybe I have an entirely wrong conception of your problem.

As I understood your original question, the model involves a set of
constant
parameters [i.e., constants that must be specified in order to generate
the
predicted m(z) values]. Trying different values of the parameters, you
have
found at least 10 sets of constants that all seem equally good (i.e.,
all give
essentially the same minimum chi-square value). So, let's say you now
have 10
different models, m_1(), m_2(), m_3() ... m_10(), all of which have the
same
structure but different values for the constant parameters.

Suppose you plot the 10 functions, m_1(z), m_2(z), ... across the range
of z
values. I am just asking whether the 10 plots are actually all
virtually
identical? If so, the parameters of the model are not identifiable.

>I wonder about your criteria for "virtual identity" of these m(z)'s.
I have no formal criterion in mind, and it depends a bit on the range
of the
observed values. I am just wondering if the different m_i(z) values are
all
quite close to each other at each of z. If you make the 10 plots on
the
same graph, you will see whether they are essentially superimposed or
not.

.