“…In this study, we estimate three different models: for reading fluency, for reading comprehension, and for arithmetic fluency based on our hypothesized models. In view of the research reviewed above, we constructed our hypothesized models (see Figure 1 for the model of reading fluency; other models were estimated with the same logic) with the expectation to find the following: (1) paths from parental reading difficulties ( Pennington and Lefly, 2001 ; Torppa et al, 2011 ; van Bergen et al, 2012 ; Hulme et al, 2015 ) and parental mathematical difficulties ( Shalev and Gross-Tsur, 2001 ; Soares et al, 2018 ) to the respective skills in children; (2) cross-domain paths from parental mathematical difficulties to children’s reading skills and from parental reading difficulties to children’s mathematical skills ( Landerl and Moll, 2010 ; Moll et al, 2015 ); (3) paths from HLE and HNE to both respective and cross-domain skills in children ( Melhuish et al, 2008 ; Anders et al, 2012 ; Kleemans et al, 2012 ; Baker, 2014 ; Napoli and Purpura, 2018 ); (4) paths from parental education to children’s skills ( Torppa et al, 2006 ; Hamilton et al, 2016 ; van Bergen et al, 2017 ); (5) paths from parental education to HLE and HNE ( Hamilton et al, 2016 ); and (6) paths from FR to the home environment ( Scarborough et al, 1991 ; Bus et al, 1995 ; Elbro et al, 1998 ; Snowling, 2000 ; Hamilton et al, 2016 ; Esmaeeli et al, 2019 ), including also the examination of the indirect relationships (FR → home environment → children’s skills), as Esmaeeli et al (2019) argued that these paths need to be tested in future studies. Finally, we expected that the paths to later skill assessments run through the early skill assessments.…”