24 S
.L. Rodriguez-Zas et al. Livestock Production Science 67 2000 19 –30
serious problem. Comparisons between non-nested high levels of SCS, causing the average to be higher
models relied on Akaike’s Information Criteria AIC; than the values usually associated to minor patho-
Akaike, 1974 and on Schwarz’s Bayesian Criterion gens. As shown in Table 1, SCS decreased to a nadir
BIC; Schwarz, 1978, both of which adjust likeli- at about 60 DIM and then increased, although not in
hood ratio tests by the number of parameters in the a monotonic fashion, without regaining the initial
model. Also, the residual variance was used to level. The standard deviation followed an inverse
compare models. pattern. All parameter estimates presented sub-
sequently are from the reduced models, as mentioned earlier. In all models, lactation number was not a
3. Results significant source of variation for any of the parame-
ters. Mean 305-day, mature equivalent milk yield was
Estimates from Wood’s model Table 2 indicate about 7600 kg. Average SCC and standard deviation
that intramammary infection status affects the two was 671,000 and 897,000 cells ml, respectively. A
shape parameters b and d . The a scale parameter few cows, with clinical mastitis symptoms, have very
was higher in infected animals, but the difference was not significant. This is sensible because the IMI
variable pertains to status during and not at the onset
Table 1 Average somatic cell score and standard deviation S.D. by
of lactation. Animals that had positive pathogen
test-day
isolations during lactation had a less sharp fall in
Days in milk Mean
S.D.
SCS at the beginning of lactation positive parameter b estimate when IMI51 than cows free of infection
14 5.425
1.418
throughout lactation. However, infected cows had
30 4.910
1.519 60
4.875 1.616
steeper rates of increase after nadir positive parame-
90 5.096
1.463
ter d estimate when IMI51 than non-infected cows.
120 5.105
1.295
The period of calving affected the shape parameters
150 5.132
1.386
significantly: cows calving in period 3 last 3 years
180 5.264
1.331
of the trial tended to have larger b and d values than
210 5.017
1.274 240
5.171 1.296
those calving at periods 1 or 2. The between-cow
270 5.163
1.357
variation was significant for parameters b and d. The
300 5.038
1.374
variance components cannot be expressed in terms of
Table 2 Parameter estimates, asymptotic standard errors S.E. and 95 confidence limits lower, upper, from Wood’s model
Parameter Estimate
S.E. Lower
Upper
a
m 5.668
0.238 5.201
6.314
a
m 20.055
0.017 20.088
20.023
b 24
24 24
24
m 23.9310
2.8310 29.1310
2.2310
d
IMI 0.055
0.010 0.035
0.075
b 24
24 24
IMI 8.4310
2.3310 4.2310
0.001
d
P 20.055
0.012 20.078
20.032
1b
P 20.035
0.011 20.056
20.014
2b 24
24
P 20.001
2.7310 20.002
29.2310
1d 24
24 24
P 29.4310
2.5310 20.001
25.1310
2d 24
Varb 0.003
4.0310 0.002
0.004
26 26
27 26
Vard 1.2310
3.8310 7.7310
3.1310
25 26
25 25
Covb, d 4.7310
8.6310 2.9310
7.7310 Vare
1.181 0.038
1.110 1.258
a
m , intercept for parameter i; IMI , effect of presence of intramammary infection; P , effect of the k period of calving as a deviation from
i i
ki
the third one; Vari , between-cow variance for parameter i; Covi, j , covariance between parameters i and j; Vare, residual variance.
S .L. Rodriguez-Zas et al. Livestock Production Science 67 2000 19 –30
25
fractional contribution to the total variance because such cows had higher levels of somatic cells when a
of the nonlinearity. The residual variance is in the minimum had been reached. All components of
SCS scale Eq. 1, whereas the components are dispersion were significant and the random effects
expressed at the level of the parameters Eq. 2. had a strong intercorrelation that could have conse-
The correlation between random effects affecting quences in selection for specific features of the SCS
parameters b and d was about 0.78, suggesting that pattern.
cows with rapid decline of SCS early in lactation With the ME model Table 4, only IMI status and
tend to regain levels slowly after nadir. cow were significant sources of variation. Infected
The presence of intramammary infection affected cows had lower values of parameter a, which means
all three parameters of the IQ model Table 3. The a higher baseline SCS level. The four parameters
infected cows had a slower rate of decrease of SCS were strongly intercorrelated, especially b and d,
in early lactation larger parameter a, and a some- which had an almost perfect correlation. This sug-
what higher rate of increase in late lactation positive gests potential computational problems at least with
estimates of parameter d than healthy cows. The the present data structure, thus estimates should be
SCS curve tended to be ‘flatter’ in the presence of interpreted with caution.
infection positive estimates of parameter d and The estimates obtained from the MG model are in
negative estimates of parameter b describing the fall Table 5. Presence of intramammary infection in-
and follow up increase in SCS levels, respectively, creased the level of somatic cell score parameter a,
in agreement with results from Wood’s model. decreased the rate of increase of SCS at 150 days
Period affected variation in b and d parameters after calving parameter b and reduced the rate of
significantly. Season of calving affected only the fall of somatic cell levels immediately after calving
scale parameter b. Cows calving in seasons 2 and 3 parameter f . Parameter b was higher in cows that
April–September had larger b parameter estimates calved in the first period and lower for cows calving
than those calving at other times; this implies that in the third period. Components of dispersion and
Table 3 Parameter estimates, asymptotic standard errors S.E. and 95 confidence limits lower, upper, from the inverse quadratic model
Parameter Estimate
S.E. Lower
Upper
a
m 20.816
0.168 21.145
20.487
a
m 0.245
0.011 0.223
0.268
b 24
25 24
26
m 21.1310
4.3310 22.1310
21.3310
d
IMI 0.582
0.190 0.209
0.955
a
IMI 20.059
0.011 20.081
20.037
b 24
25 24
24
IMI 1.6310
4.2310 1.4310
2.1310
d
P 0.037
0.008 0.022
0.052
1b
P 0.021
0.007 0.007
0.034
2b 24
25 24
24
P 21.8310
3.5310 22.3310
21.1310
1d 24
25 24
2
P 21.1310
3.2310 22.1310
21.0310 4
2d
S 20.002
0.005 20.012
0.008
1b 24
S 1.8310
0.006 20.011
0.012
2b
S 0.028
0.006 0.017
0.039
3b
Vara 0.563
0.129 0.376
0.933
24
Varb 0.003
4.7310 0.002
0.004
28 28
28 28
Vard 3.1310
1.1310 1.9310
5.6310 Cova, b
20.031 0.007
20.044 20.017
25 25
25 24
Cova, d 7.6310
2.5310 3.6310
1.2310
26 26
26 25
Covb, d 27.4310
3.5310 25.1310
21.1310 Vare
1.102 0.037
1.031 1.178
a
m , intercept for parameter i; IMI , effect of presence of intramammary infection; P , effect of the k period of calving as a deviation from
i i
ki
the third one; S , effect of the k season of calving as a deviation from the fourth one; Vari , variance for parameter i; Covi, j , covariance
ki
between parameters i and j; Vare, residual variance.
26 S
.L. Rodriguez-Zas et al. Livestock Production Science 67 2000 19 –30 Table 4
Parameter estimates, asymptotic standard errors S.E. and 95 confidence limits lower, upper, from the Mitscherlich-exponential model Parameter
Estimate S.E.
Lower Upper
a
m 23.581
0.129 23.834
3.328
a 24
m 0.004
0.002 1.0310
0.009
b 24
m 0.004
0.002 24.1310
0.008
d
IMI 20.529
0.104 20.733
20.325
a
Vara 1.314
0.219 0.972
1.877
24 24
24 24
Varb 5.1310
1.0310 4.1310
8.3310
24 25
24 24
Vard 4.7310
9.2310 3.0310
7.2310 Cova, b
20.016 0.004
20.024 20.008
Cova, d 20.016
0.004 20.024
20.008
24 25
24 24
Covb, d 4.9310
9.7310 3.3310
7.1310 Vare
1.095 0.037
1.025 1.172
a
m , intercept for parameter i; IMI , effect of presence of intramammary infection; Vari, variance for parameter i; Covi, j, covariance
i i
between parameters i and j; Vare, residual variance. Table 5
parameter a would be expected to have a more
Parameter estimates, asymptotic standard errors S.E. and 95
variable rate of increase of SCS in the middle of
confidence limits lower, upper, from the Morant and Gnanasak-
lactation.
thy’s model
Fixed factors were not a significant source of
Parameter Estimate
S.E. Lower
Upper
variation in any of the linear regression parameters
a
m 4.292
0.120 4.057
4.526
a
of Ali and Schaeffer’s model, but there was signifi-
m 0.060
0.022 0.016
0.104
b
cant variation and covariation between cows. In
24
m 20.020
0.011 20.040
9.1310
d
Wilmink’s model, presence of intramammary in-
m 4.737
0.814 3.139
6.334
f
fection was associated with higher levels of SCS
IMI 0.853
0.137 0.584
1.121
a
IMI 20.074
0.021 20.115
20.034
during lactation, in agreement with W, IQ and MG
b
IMI 22.791
0.860 24.478
21.105
f
models. Cows calving on the first and second periods
P 0.096
0.019 0.060
0.132
1b
had lower a values than those calving in the third
P 0.062
0.017 0.029
0.096
2b
period, and higher increases in SCS levels in mid
Vara 0.742
0.093 0.589
0.964
and late lactation. There was significant variation
Varb 0.006
0.001 0.004
0.009 Vard
0.008 0.001
0.005 0.011
between cows for parameters of this model.
Cova, b 0.008
0.007 20.005
0.022
Numerical values of end-points used for compar-
Cova, d 20.049
0.010 20.069
20.030
ing models are in Table 6. The Ali and Schaeffer’s
24 24
Covb, d 20.001
8.6310 20.003
5.2310 Vare
1.043 0.035
0.977 1.116
Table 6
a
m , intercept for parameter i; IMI , effect of presence of
i i
Comparison between models intramammary infection; P , effect of the k period of calving as a
ki a
b
Model MSE
LIK AIC
BIC deviation from the third one; Vari , variance of parameter i;
Covi, j , covariance between parameters i and j; Vare, residual W
1.181 27784.017
23896.01 23907.56
variance. IQ
1.102 27803.159
23908.58 23928.78
MG 1.043
27640.905 23827.45
23847.66 ME
1.095 27720.616
23867.31 23887.52
co-dispersion for parameters a, b and d were signifi-
AS 0.950
27644.072 23838.04
23884.24
cant indicating differences between cows in the
WI 1.098
27707.943 23860.97
23881.18
shape and scale of SCS lactation curves. In spite of
a
W, Wood’s; IQ, inverse quadratic; MG, Morant and Gnanasak-
being a four-parameter model, the correlation struc-
thy’s; ME, Mitscherlich-exponential; AS, Ali and Schaeffer’s; WI,
ture between random effects was weaker than for the
Wilmink’s model.
other models. Only random effects affecting parame-
b
MSE, residual variance; LIK, 23maximized restricted log-
ters a and d had a sizable 20.64 correlation,
likelihood; AIC, Akaike’s information criterion; BIC, Schwarz’s
suggesting that cows with a lower baseline SCS
information criterion.
S .L. Rodriguez-Zas et al. Livestock Production Science 67 2000 19 –30
27
AS model had the lowest residual variance, but the the second most common quarter isolation in the
largest number of parameters; the ME model was Hogan et al. 1989 study, but the number of
second and the one with the poorest fit in the MSE infected quarters ranged between 1 calving and
sense, was Wood’s. The MG model had the largest 8.8 drying off, the latter being close to the
maximized restricted likelihood, followed by AS. incidence found in this data set. An improvement in
Based on Akaike’s and Schwarz’s criteria, the MG the management-health conditions during the study
model was better, followed by AS or WI, depending may be reflected by the lower rate of increase of SCS
on the criterion considered. The residuals plots did found in the third period of calving MG model and
not exhibit any patterns, suggesting that the model by the lower predicted values for this period W
assumptions were suitable. model. The relatively warm and humid conditions
during peak lactation experienced by cows calving between July and September may have facilitated
4. Discussion contamination and prevalence of pathogens. This
