With no check engine light (CEL) , might be a little tough to find.
1) Try going to an auto parts chain store that reads codes and see if there are any pending codes in the P03XX series, engine misfire detected. the 'xx' will be 00 for a random misfire, or 01 - 10 if it is a specific cylinder. (ie: code P0304 means a misfire on cylinder 4) This can pinpoint an ignition issue, or help find a vacuum leak. (this P03XX series is OBD2 mandated, so any code reader can see it. Not like the factory diagnostic codes.. >( )
2) the Mass Airflow Sensor (MAF) is after the air filter, and sometimes when a dirty one is removed particles get past and clog it. There is a simple spray that cleans it,( https://www.walmart.com/ip/CRC-Industries-05110-Mass-Air-Flow-Sensor-Cleaner-Wt-11-oz/39950006?wmlspartner=wlpa&selectedSellerId=1122&adid=22222222227028232711&wl0=&wl1=g&wl2=c&wl3=60525702969&wl4=pla-95221774089&wl5=9011833&wl6=&wl7=&wl8=&wl9=pla&wl10=101593696&wl11=online&wl12=39950006&wl13=&veh=sem&gclid=EAIaIQobChMIiN2RhIbk4gIVj56fCh2hEA6wEAQYASABEgKNTfD_BwE ) and that has solved rough idle issues before. Can help fuel mileage too. Might be a pending code in the P017X series if this is the case.
(https://www.aa1car.com/library/maf_sensor_ford.gif)
""CLEANING FORD MAF SENSORS
For some reason, Ford vehicles have had a history of MAF sensor problems caused by contamination. In some cases, dirt gets past a leaky air filter and fouls the sensor wire. In other cases, carbon varnish builds up on the sensor from fuel vapors backing up through the intake manifold. Either way, contamination makes the MAF sensor sluggish, and often sets a P0171 or P0174 lean code.
The fix is to clean the sensor element with aerosol electronics cleaner (CRC makes a good product for this). The MAF sensor is located inside the air filter housing on some applications (Windstar, for example) or between the air filter and throttle body. Spray the sensor element with electronics cleaner, let it soak for about 10 minutes, then repeat. DO NOT use any other type of cleaner as this may damage the sensor. Also, DO NOT touch, scrub or attempt to physically clean the sensor element as this too can ruin the sensor.""
source - https://www.aa1car.com/library/maf_sensors.htm
(When I clean them, I will give them 4-5 soak-wait-rinse cycles with the spray. Do something else while you wait, or you will rush the process. May take 45 min to an hour total. I do this task thoroughly ONCE, as I do NOT like come-backs from customers. )
3) a slow acting IAC (Idle Air Controller) can also cause rough idle, but really requires a scan tool to properly diagnose. Or you can be a shadetree mechanic and just throw parts at it until something works. :lol
My top 3 guesses. :-D In order. If no CEL or pending codes, I would look at cleaning the MAF, especially after the problem seemed to arrive after a dirty air filter change.
Good Luck!