Five anthraquinone dyes with bis(4-propylphenyl) substituents, connected via sulfide or amine linking groups at the 1,5-positions or directly at the 2,6-positions, have been studied as guests in the nematic liquid crystal host, E7. Polarized UV-visible absorption spectra of aligned samples were used to obtain experimental dichroic order parameters, which exhibit values in the range 0.51-0.74. Fully atomistic MD simulations of these guest-host systems were carried out, generally using default parameters but using new force constants derived here for the dyes containing flexible phenyl-sulfide and phenyl-amine linking groups. An analysis of the alignment of the dye molecules in these simulations provides calculated molecular order parameters, which are combined with calculated order parameters for the alignment of the transition dipole moments within the dyes, reported previously, to give calculated dichroic order parameters. The trend in the calculated dichroic order parameters between the dyes shows a good match with the trend in the experimental values, enabling the observed variation to be rationalised primarily by changes in the alignment of the calculated transition dipole moments within the dyes; the calculated molecular order parameters show a relatively small variation between the dyes. The results indicate that this computational approach may be used generally to rationalise trends in the alignment of guest molecules in liquid crystal hosts, suggesting that it may also be able to provide a predictive aid in the design of guest dyes.