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    PATH ANALYSIS MODEL

    L Tn Phng*

    1.Cc m hnh thnh phn ca Path (Elemental Models)Hnh 1 minh ha 3 m hnh thnh phn c bn ca m hnh Path

    Hnh 1: Cc m hnh thnh phn ca path

    *Bc s, Thc s Y t cng cng

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    Hnh 2: Cc v d v kiu m hnh path

    3.Cc iu kin nh hnh m hnh pathM hnh nh hnh c (identified) th mi c th tin hnh cc bc phn tch tip theo. C 2 iu

    kin chung mt m hnh SEM ni chung nh hnh c:

    - t do ca m hnh phi ln hn zero.- Tt c cc bin n (latent variables), bao gm c phn d D, phi gn vi mt thang o.

    3.1 t do ca m hnh t do ca m hnh c tnh ton nh sau: df = p(p+1)/2 - k. Trong p l s bin quan st

    trong m hnh, v k l s tham s cn phi c lng.

    Khi df = 0, ta gi l m hnh nh hnh va ng (just-identified)

    Khi df>0, ta gi l m hnh nh hnh qu (overidentified)

    3.2Thang o cho bin n (Scaling latent variables)3.2.1Thang o cho s d

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    S d D (sai s) ca bin ph thuc l bin n (latent variable). Thang o cho bin n ny thng s

    dng l thang o nh dng ti n v (unit loading identification: ULI) vi h s phn d cha chun

    ha (unstandardized residucal path coefficient) c c nh bng 1.Trong s m hnh, h s ny

    c biu th bng s 1 nm bn cnh mi tn t bin D n bin Y. Mc d ta c th n nh h s

    ny cho mt s dng bt k, nhng mc nh thng chn 1.

    3.2.2Thang o cho yu t (factor)C 2 phng php p dng thang o cho cc yu t trong m hnh (cn gi l cu trc: construct)

    - S dng ULI nh i vi phn d trn. C ngha l c nh bng 1 cho mt h s chachun ha (unstandardized coefficient) ca mt trong s cc bin c lp ca yu t . V

    d, A l yu t gm c 4 bin c lp cu to nn n: X1, X2, X3, X4. Ta c th c nh h s

    tc ng ca X1 ln A bng 1. Lc ny, bin c lp b gn h s bng 1 gi l bin tham

    chiu (reference variable) hoc bin nh du (marker variable). Vi v d va ri th X1 l

    bin tham chiu.

    - C nh phng sai ca yu t bng mt hng s. C th s dng bt c s dng nolm hng s ny, nhng thng l s dng tng t ULI nh trn, v do phng sai ca

    yu t s bng 1. Trong trng hp ny, thay v gi l ULI th c gi l UVI (unit variancve

    identification).

    3.3Cc quy tc nh hnh m hnh (model identification)3.3.1M hnh recursiveTt c m hnh dng recursive u mc nhin c nh hnh

    3.3.2M hnh nonrecursiveKhng phi tt c cc m hnh nonrecursive u nh hnh c. Tnh cht v s iu kin nh

    hnh cc m hnh nonrecursive ph thuc vo cc mi lin h gia cc bin d D. Cc iu kin ny

    tng i phc tp cho nn s khng c trnh by trong bi vit ny. Chi tit ca cc iu kin

    ny c th tham kho ti liu ca Kline, third edition, trang 132-137.

    4.c lng Maximum Likelihood (ML Estimation)c lng Maximum Likelihood (ML) l phng php c lng ph bin v c p dng mc

    nh cho hu ht cc phn mm SEM. Do , ML s c trnh by chi tit cho m hnh path.

    ML l phng php ph bin nht. Phng php ny gi nh rng cc bin ph thuc ni sinh

    (endogenous variable) phi l bin lin tc c phn phi bnh thng. Nu khng tho mn gi nh

    ny cn phi p dng phng php c lng khc thay th.

    4.1Gi tr ban u

    ML lin quan n hng lot cc th thut tnh ton ca my tnh c thc hin lp i lp li cho

    ra kt qu cui cng l mt m hnh ph hp. Khi s dng cc phn mm chy SEM, my tnh s bt

    u vi mt gi tr ban u, ri sau s lp li lin tc cc tnh ton tip theo ci thin m hnh.

    Nu khng tm thy m hnh thch hp, phn mm s thng bo li v m hnh tht bi. Mi phn

    mm SEM u c ci t mc nh mt gi tr ban u cho ML. Tuy nhin, trong nhng trng hp

    m hnh phc tp, c th s dng gi tr ban u khc vi gi tr mc nh ca phn mm. Ngoi ra,

    c th nng s ln chy tnh ton ca phn mm, v d nh t 30 ln ln 100 ln.

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    4.2Cc gi nh ca MLML bao gm cc gi nh cn phi tho mn nh sau:

    - Gi tr cc bin cha c chun ho (unstandardized variables)- Khng c s hin din ca d liu trng (missing value). Tuy nhin, iu kin ny c th

    c tho mn bng cch s dng cc phng php x l d liu trng (listwise, pairwise,

    MI hoc EM).

    - Tnh c lp ca cc bin c lp ngoi sinh (exogenous) v khng c sai s- Phn phi bnh thng ca cc bin ph thuc ni sinh (endogenous).

    Hai gi nh sau cng tng t nh gi nh trong phn tch a bin.

    4.3Gii thch cc tham s c lng- Cc h s m hnh c gii thch ging nh cc h s hi quy trong phn tch a bin.- Phng sai ca phn d trong m hnh cha chun ho c gii thch l phn phng sai

    khng l gii c ca bin ph thuc ni sinh tng ng. Phn ny tng t nh cch gii

    thch R2 ca phn tch a bin.

    4.4V d c th v c lng cho mt path modelV d sau y lin quan n mt m hnh tm hiu tc ng ca mi quan h gia gio vin v hc

    sinh (Teacher-Pupil interaction) n tnh trng th lc (somatic status) v tri nghim hc ng

    (school experience) ca hc sinh. Tri nghim hc ng hm hc sinh c thy thch th, phn

    khi khi n trng hay khng. M hnh cho rng mi quan h gia gio vin v hc sinh ch nh

    hng bi 3 yu t khc: (1) S h tr ca nh trng (school support) i vi gio vin, (2) ch

    k lut (coercive control), v (3) Tnh trng p lc cng thng ca gio vin (teacher burnout). Ngoi

    ra, s h tr ca nh trng v ch k lut cng nh hng n tnh trng p lc cng thng ca

    gio vin. M hnh c minh ha trong Hnh 3.

    Hnh 3: M hnh path v nguyn nhn v hu qu ca mi quan h gia gio vin v hc sinh

    Phn tch m hnh trn bng c lng ML, kt qu cho thy nh Hnh 4.

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    Hnh 4: M hnh path recursive v nguyn nhn v hu qu ca mi quan h gia gio vin v hc sinh. Ccc lng chun ho cho phn d (D)

    Xem xt kt qu ny:

    - t do ca m hnh: C tt c 6 bin (quan st) trong m hnh (p = 6), v c 14 tham scn c lng (k = 14). Vy t do ca m hnh l: df = p(p+1)/2-k = 7.

    - Do m hnh l m hnh recursive, cho nn n mc nhin c nh hnh (idetification).- Cc h s tng quan (correlation) v lch chun ca s liu c th hin Bng 1.

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    - Tc gi Kline s dng phn mm LISREL c lng tham s bng phng php ML. Ktqu th hin ti Bng 2.

    Bng 1: S liu u vo (Input data) v tng quan v lch chun cho phn tch m hnh v nguyn nhnv hu qu ca mi quan h gia gio vin v hc sinh

    Bng 2: c lng ML cho m hnh v nguyn nhn v hu qu ca mi quan h gia gio vin v hc sinh

    4.4.1Cc tc ng trc tip (direct effects)Xt kt qu tc ng (trc tip) cha chun ho ca s h tr ca nh trng (school support) i

    vi s cng thng ca gio vin (teacher burnout) ti Bng 2 cho thy h s c lng l -0.384. H

    s ny cng th hin trong Hnh 4(a). H s ny c gii thch nh sau: Khi tng ln 1 im ca sh tr nh trng s lm gim i 0.384 im ca s cng thng ca gio vin vi iu kin im ca

    ch k lut (coercive control) khng i. Sai s chun (SE) ca h s ny l 0.079 (Bng 2), cho

    nn z = -0.384/0.079=4.86. Gi tr 4.86 vt qu ngng 2.58 cho mt ngha thng k mc

    0.01. Cc h s cha chun ho khc c gii thch tng t.

    Tuy nhin, c th v cc thang o l khng ng nht, cho nn vic so snh trc tip l khng th

    c. Do , cn phi chun ho cc thang o.

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    i vi kt qu chun ho (standardized, Bng 2, Hnh 4(b)), h s chun ho cho tc ng trc tip

    ca s h tr ca nh trng (school support) v ch k lut (coercive control) n s cng thng

    ca gio vin (teacher burnout) ln lt l -0.413 v 0.250. Cc h s ny c gii thch nh sau:

    Khi mc nh trng h tr tng ln 1 lch chun trn mc trung bnh s tin on cng thng

    ca gio vin gim i 0.413 lch chun., vi iu kin ch k lut l khng i. Tng t, nu

    tng ln 1 lch chun trn mc trung bnh ca ch k lut s tin on tng ln 0.25 lch

    chun ca s cng thng ca gio vin, vi iu kin mc nh trng h tr khng i. Tc ng

    ca s h tr nh trng ln hn gp 1 v ln so vi tc ng ca ch k lut (0.413/0.250).

    Cc gii thch khc l tng t.

    4.4.2Phng sai ca phn d (Disturbance Variance)c lng phng sai ca phn d phn nh s bin thin khng th l gii c ca bin ph

    thuc ni sinh (endogenous) tng ng. V d, phng sai phn d cha chun ho ca bin tnh

    trng th lc (somantic status) l 13.073 (Bng 2). Phng sai mu (sample variance) ca bin ny

    c tnh bng s2 = 5.27142 = 27.788 (5.2514 l SD ca bin ny ti Bng 1). T l gia phng sai

    phn d v phng sai mu ca bin ny l 13.073/27.788 = 0.470. Con s ny c ngha l t l ca

    phng sai quan st c trong bin ny khng th l gii c bi tc ng trc tip ca quan h

    gio vin hc sinh i vi tnh trng th cht ca hc sinh l 47%. Nh vy, m hnh tc ng trc

    tip ca quan h gio vin hc sinh i vi tnh trng th cht ca hc sinh (Hnh 4) gii thch cho R2

    = 1-0.47 = 0.530 s bin thin ca bin tnh trng th cht hc sinh.

    Cc phng sai phn d khc c gii thch tng t.

    4.4.3Cc tc ng gin tip (Indirect effects)H s cc tc ng gin tip c tnh bng tch s ca cc tc ng trc tip c lin quan, k c

    chun ho hay cha chun ho. V d tc ng gin tip chun ho ca s h tr ca nh trng

    (school support) ln tri nghim hc ng (school experience) ca hc sinh, thng qua yu t trung

    gian l quan h gia gio vin v hc sinh, c tnh bng tch s ca 2 h s trc tip lin quan, tcl bng 0.203 x 0.654 = 0.133 (Hnh 4(b)). Kt qu 0.133 c gii thch l mc tri nghim hc

    ng ca hc sinh c tin on l tng ln 0.133 lch chun cho mi khi tng ln 1 lch

    chun ca s h tr nh trng thng qua trung gian mi quan h gia gio vin v hc sinh. Cc h

    s cha chun ho cng c gii thch tng t.

    4.4.4Tc ng ton th (total effects)Tc ng ton th l tng ca cc tc ng trc tip v gin tip ca mt bin ny ln mt bin khc.

    V d, tc ng ton th chun ha ca s h tr trng hc (school support) ln mi quan h gia

    gio vin v hc sinh, thng qua trung gian ca bin s cng thng ca gio vin, l tng ca cc

    tc ng trc tip v gin tip nh sau: 0.203 + (-0.413) + 0.278 = 0.88. Cch gii thch cng tng tnh trn.

    5.Th nghim gi thuyt m hnh (Hypothesis Testing)y l giai on th nghim m hnh c ph hp vi cc d liu ca mu hay khng (fit the sample

    data), ng thi xem xt n cc m hnh tng ng hoc thay th. Mt nhn thc cha ng

    hay gp ca mt s nh nghin cu cho rng mc ch cui cng ca SEM l tm ra c mt m

    hnh ph hp. Tht ra, ngay c mt m hnh khng ph hp cng