A Labor Market Analyst will likely appear by phone at the request of the Administrative Law Judge. Labor Market Analysts are often used to determine if an offer of employment was "legitimate" (most commonly to answer the question of whether the pay rate offered was appropriate in the market) for purposes of determining eligibility for unemployment benefits if a job offer was denied.
Without additional facts, it is difficult to determine if continued pursuit of the benefits is likely to be successful. You may want to consider consulting with an attorney who is experienced with unemployment benefits.
I doubt that an actual "labor market analyst" will be present. Usually at these hearings a report from a labor market analyst is used to show statistics in aiding the ALJ in determining whether you're eligible for benefits. You don't provide enough information on your claim (i.e., whether you quit or were terminated, etc.). If you want to collect UI benefits then you have to be prepared to battle it out in hearings. Perhaps hiring an attorney is best.