MeSH (Medical Subject Headers):
The first step to uncovering level of insurance payout for children's mental health assessment and diagnosis is to define the procedure. To do this you will need the CPT (Current Procedural Terminology) code.
You will then need to figure out the cost of each procedure
Note the complexity of how Psychotherapy is defined i.e. Behavior Identification Assessment (0359T)
Allowable Amount - The maximum dollar amount that an insurer will consider reimbursing for a covered service or procedure. This dollar amount may not be the amount ultimately paid to the member or provider as it may be reduced by any co-insurance, deductible or amount beyond the annual maximum. Some plans may refer to the "allowable amount" as the "maximum allowable amount"; these terms have a similar meaning.
I was able to locate only data of state based insurance policies, and not private policies at the level of granularity needed to research CPT code coverage for Pychotherapy (see Parity or Disparity... p. 47-49) Medicaid data is available through Medicaid Analytical eXtract (MAX), but this would be very difficult to access without significant IRB approval.
My thoughts, as noted by Turner (2013, p.12) is that the problem of child assessment and diagnosis of mental illness is tied to type of coverage:
My estimates suggest that a child with a mental health disorder is twice as likely to receive a diagnosis when covered by a FFS [Fee for Service] policy relative to receiving services through an HMO.
Children enrolled in a PCCM [Primary Care Case Management] plan are three times less likely to receive a mental health diagnosis from their PCP [Primary Care Physician] (relative to FFS enrollment).