We use three different data sets, specifically $H(z)$ measurements from cosmic chronometers, the HII-galaxy Hubble diagram, and reconstructed quasar-core angular-size measurements, to perform a joint analysis of three flat cosmological models: the $R_{rm h}=ct$ Universe, $Lambda$CDM, and $w$CDM. For $R_{rm h}=ct$, the 1$sigma$ best-fit value of the Hubble constant $H_0$ is $62.336pm1.464$ $mathrm{km s^{-1} Mpc^{-1}}$, which matches previous measurements ($sim 63$ $mathrm{km s^{-1} Mpc^{-1}}$) based on best fits to individual data sets. For $Lambda$CDM, our inferred value of the Hubble constant, $H_0=67.013pm2.578$ $mathrm{km s^{-1} Mpc^{-1}}$, is more consistent with the ${it Planck}$ optimization than the locally measured value using $mbox{Cepheid}$ variables, and the matter density $Omega_{rm m}=0.347pm0.049$ similarly coincides with its ${it Planck}$ value to within 1$sigma$. For $w$CDM, the optimized parameters are $H_0=64.718pm3.088$ $mathrm{km s^{-1} Mpc^{-1}}$, $Omega_{rm m}=0.247pm0.108$ and $w=-0.693pm0.276$, also consistent with ${it Planck}$. A direct comparison of these three models using the Bayesian Information Criterion shows that the $R_{rm h}=ct$ universe is favored by the joint analysis with a likelihood of $sim 97%$ versus $lesssim 3%$ for the other two cosmologies.
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