# structural relation
mineral_phase <~ 1*clay_mineralogy_PC1 + clay_mineralogy_PC2

# structural relation
CUE ~ a1*pH +  a2*F.A_ratio + a3*CN_soil  
F.A_ratio ~ 1+ b1*pH + b2*landuse 
pH ~ 1+ c1*landuse + c2*mineral_phase
CN_soil ~ 1+ d1*landuse + d2*mineral_phase

# variances & covariances
pH ~~ pH
CUE ~~ CUE
CN_soil ~~ CN_soil
F.A_ratio ~~ CN_soil
pH ~~ CN_soil

indirect.landuse.pH := c1*a1
indirect.landuse.CN_soil := d1*a3
indirect.landuse.FA := b2*a2 + b1*c1*a2
total.landuse := indirect.landuse.pH + indirect.landuse.CN_soil + indirect.landuse.FA

indirect.mineralphase.pH := c2*a1
indirect.mineralphase.CN_soil := d2*a3
indirect.mineralphase. FA := b1*c2*a2
total.mineralphase := indirect.mineralphase.pH + indirect.mineralphase.CN_soil + indirect.mineralphase.FA

+proj=laea +lat_0=45 +lon_0=-100 +x_0=0 +y_0=0 +ellps=sphere +units=m +no_defs

PROJCRS["Sphere_ARC_INFO_Lambert_Azimuthal_Equal_Area",
    BASEGEOGCRS["GCS_Sphere_ARC_INFO",
        DATUM["D_Sphere_ARC_INFO",
            ELLIPSOID["Sphere_ARC_INFO",6370997,0,
                LENGTHUNIT["metre",1,
                    ID["EPSG",9001]]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["Degree",0.0174532925199433]]],
    CONVERSION["unnamed",
        METHOD["Lambert Azimuthal Equal Area (Spherical)",
            ID["EPSG",1027]],
        PARAMETER["Latitude of natural origin",45,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",-100,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["False easting",0,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",0,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["(E)",east,
            ORDER[1],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]],
        AXIS["(N)",north,
            ORDER[2],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]]]