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tokens: reduced χ 2 values determined from GRB data alone are around unity for all models (being between 1.03 and 1.06), while those values determined from the H ( z ) + BAO data combination range from 0.48 to 0.53, with the lower reduced χ 2 here being due to the H ( z ) data (that probably have overestimated error bars). As discussed in Ryan et al. ( 2019 ) and Cao et al. ( 2020 ), the cases that involve H ii G and QSO-AS data have a larger reduced χ 2 (between 2.11 and 3.02), which is probably due to underestimated systematic uncertainties in both cases. Based on the AIC and the BIC (see Table 1 ), the flat ΛCDM model remains the most favoured model, across all data combinations, among the six models we study. 14 From ΔAIC and ΔBIC, we find mostly weak or positive evidence against the models we considered, and only in a few cases do we find strong evidence against them. According to ΔBIC, the evidence against non-flat XCDM is strong for the H ii G, QSO-AS, and GRB only cases, and very strong for the HQASG and HzBHQASG cases. Similarly, the evidence against flat φCDM is strong for the HQASG and HzBHQASG cases, and the evidence against non-flat φCDM is strong for the H ii G, QSO-AS, and GRB only cases, and very strong for the HQASG and HzBHQASG cases. Among these six models, a comparison of the ΔBIC values from Table 1 shows that the most disfavoured model is non-flat φCDM, and that the second most disfavoured model is non-flat XCDM. This is especially true when these models are fitted to the HQASG and HzBHQASG data combinations, in which cases non-flat φCDM and non-flat XCDM are very strongly disfavoured. These models are not as strongly disfavoured by the AIC, however; from a comparison of the ΔAIC values in Table 1 , we see that the evidence against the most disfavoured model (non-flat φCDM) is only positive. 6 CONCLUSION We find that cosmological constraints determined from higher z GRB, H ii G, and QSO-AS data are mutually consistent. It is both reassuring and noteworthy that these higher z data jointly favour currently accelerating cosmological expansion, and that their constraints are consistent with the constraints imposed by more widely used and more restrictive H ( z ) and BAO data. Using a data set consisting of 31 H ( z ), 11 BAO, 120 QSO-AS, 153 H ii G, and 119 GRB measurements, we jointly constrain the parameters of the GRB Amati relation and of six cosmological models. The GRB measurements are of special interest because they reach to z ∼ 8.2 (far beyond the highest z ∼ 2.3 reached by BAO data) and into a much less studied area of redshift space. Current GRB data do not provide very restrictive constraints on cosmological model parameters, but in the near future we expect there to be more GRB observations (Shirokov et al. 2020 ) that should improve the GRB data and provide more restrictive cosmological constraints. Some of our conclusions do not differ significantly between models and so are model independent. In particular, for the