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Modelling of impedance spectroscopy (IS) data of electroceramics depends critically on the correct choice of equivalent electrical circuit so that the extracted parameters have physical significance. The strategy proposed to choose the correct circuit involves analysis of IS data in several of the four complex formalisms: impedance, electric modulus, admittance and permittivity together with consideration of the frequency and temperature dependence of data and the magnitude and temperature dependence of extracted resistance and capacitance values. This is demonstrated using IS data from oxide-ion conducting La0.80Sr0.20Ga0.83Mg0.17O2.82 ceramics over the range 182 to 280°C. Low temperature data are fitted first, to allow a full characterisation of the bulk response; some of the bulk parameters may then be fixed to enable fitting of the higher temperature data which increasingly feature lower frequency phenomena such as grain boundary impedances. The most appropriate circuit in this case is found to consist of a parallel combination of a resistor, capacitor and constant phase element (CPE) for the bulk response in series with a resistor and capacitor in parallel for a constriction resistance. The origin of the constriction resistance may be associated with the presence of plate-like LaSrGaO4 secondary phase within the grains and/or with the presence of pores at the grain boundaries. The importance of choosing (a) the correct equivalent circuit and (b) approximately correct input values for the various circuit parameters to be fitted and refined are demonstrated. [ABSTRACT FROM AUTHOR]