For more than a decade total solar irradiance has been monitored simultaneously from space by different satellites. The detection of total solar irradiance variations by satellite-based experiments during the past decade and a half has stimulated modeling efforts to help identify their causes and to provide estimates of irradiance data, using ‘proxy’ indicators of solar activity, for time intervals when no satellite observations exist. In this paper total solar irradiance observed by the Nimbus-7/ERB, SMM/ACRIM I, and UARS/ACRIM II radiometers is modeled with the Photometric Sunspot Index and the Mg II core-to-wing ratio. Since the formation of the Mg II line is very similar to that of the Ca II K line, the Mg core-to-wing ratio, derived from the irradiance observations of the Nimbus-7 and NOAA9 satellites, is used as a proxy for the bright magnetic elements. It is shown that the observed changes in total solar irradiance are underestimated by the proxy models at the time of maximum and during the beginning of the declining portion of solar cycle 22 similar to behavior just before the maximum of solar cycle 21. This disagreement between total irradiance observations and their model estimates is indicative of the fact that the underlying physical mechanism of the changes observed in the solar radiative output is not well-understood. Furthermore, the uncertainties in the proxy data used for irradiance modeling and the resulting limitation of the models should be taken into account, especially when the irradiance models are used for climatic studies.