In March that group said AMs' pay should be brought more into line with that of MPs to reflect the assembly's new law making responsibilities.
The near £4,000 increase brought the salary of a backbench AM to more than £50,000 a year.
Currently, members may claim an allowance of up to £15,000 to run their office.
Another allowance, up to £13,000, is available to help AMs who live away from the Cardiff area to stay overnight or find a second home in the capital.
The panel will also examine payments for support staff, IT and constituency accommodation
Sir Roger said: "The National Assembly for Wales has at its core a commitment to transparent and accessible democracy."
"I am proud to chair a panel that will report to the Assembly Commission on the best way of providing support to Assembly Members that is appropriate for Wales, and that will help underpin future good governance and effective public service in Wales."
But the campaign group, the Taxpayers' Alliance, said that AMs should show they understand the problems faced by constituents and turn down any increases.
REVIEW GROUP PANEL
Sir Roger Jones, Swansea University pro-chancellor
Dafydd Wigley, former Plaid leader
Nigel Rudd, former chief executive of the East Midlands Regional Assembly
Deep Sagar, Chair of the NHS 24 service in Scotland
Jackie Nickson, HR manager, Opagus Group
Mark Wallace, campaign director for the group said: "From our point of view, taxpayers are under a lot of pressure at the moment given the record tax take and the current economic conditions.
"People are very concerned that our elected representatives are in some cases squandering our money and at the very worse helping themselves to money they're not entitled to.
"The best way to restore the publics faith and dispel those concerns is to make the system 100% transparent by publishing all expenses claims and receipts for everyone to see," he added.
Claire Clancy, the chief executive of the Assembly Commission said there had been "a significant public debate" about how politicians were paid and supported for their work.
"The Independent Review Panel has therefore been tasked to produce a set of evidence-based recommendations containing principles that will deliver a fair, equitable and transparent process for the financial support of Assembly Members in order to improve public knowledge and perception of these issues," she said.
The members of the review group include Dafydd Wigley, the former Plaid leader, but also representatives from business and the public sector outside Wales.
The group is expected to report back before the end of next March to the Assembly Commission, the body responsible for providing property, staff and services to AMs.
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